共查询到20条相似文献,搜索用时 640 毫秒
1.
Let \(\varphi \) be an arbitrary linear-fractional self-map of the unit disk \({\mathbb {D}}\) and consider the composition operator \(C_{-1, \varphi }\) and the Toeplitz operator \(T_{-1,z}\) on the Hardy space \(H^2\) and the corresponding operators \(C_{\alpha , \varphi }\) and \(T_{\alpha , z}\) on the weighted Bergman spaces \(A^2_{\alpha }\) for \(\alpha >-1\). We prove that the unital C\(^*\)-algebra \(C^*(T_{\alpha , z}, C_{\alpha , \varphi })\) generated by \(T_{\alpha , z}\) and \(C_{\alpha , \varphi }\) is unitarily equivalent to \(C^*(T_{-1, z}, C_{-1, \varphi }),\) which extends a known result for automorphism-induced composition operators. For maps \(\varphi \) that are not automorphisms of \({\mathbb {D}}\), we show that \(C^*(C_{\alpha , \varphi }, {\mathcal {K}}_{\alpha })\) is unitarily equivalent to \(C^*(C_{-1, \varphi }, {\mathcal {K}}_{-1})\), where \({\mathcal {K}}_{\alpha }\) and \({\mathcal {K}}_{-1}\) denote the ideals of compact operators on \(A^2_{\alpha }\) and \(H^2\), respectively, and apply existing structure theorems for \(C^*(C_{-1, \varphi }, {\mathcal {K}}_{-1})/{\mathcal {K}}_{-1}\) to describe the structure of \(C^*(C_{\alpha , \varphi }, {\mathcal {K}}_{\alpha })/\mathcal {K_{\alpha }}\), up to isomorphism. We also establish a unitary equivalence between related weighted composition operators induced by maps \(\varphi \) that fix a point on the unit circle. 相似文献
2.
3.
Motivated by applications in the field of shape analysis, we study reparametrization invariant, fractional order Sobolev-type metrics on the space of smooth regular curves \(\mathrm {Imm}(\mathrm {S}^{1},\mathbb {R}^d)\) and on its Sobolev completions \({\mathcal {I}}^{q}(\mathrm {S}^{1},{\mathbb {R}}^{d})\). We prove local well-posedness of the geodesic equations both on the Banach manifold \({\mathcal {I}}^{q}(\mathrm {S}^{1},{\mathbb {R}}^{d})\) and on the Fréchet-manifold \(\mathrm {Imm}(\mathrm {S}^{1},\mathbb {R}^d)\) provided the order of the metric is greater or equal to one. In addition we show that the \(H^s\)-metric induces a strong Riemannian metric on the Banach manifold \({\mathcal {I}}^{s}(\mathrm {S}^{1},{\mathbb {R}}^{d})\) of the same order s, provided \(s>\frac{3}{2}\). These investigations can be also interpreted as a generalization of the analysis for right invariant metrics on the diffeomorphism group. 相似文献
4.
Let \({\mathcal L}\equiv-\Delta+V\) be the Schrödinger operator in \({{\mathbb R}^n}\), where V is a nonnegative function satisfying the reverse Hölder inequality. Let ρ be an admissible function modeled on the known auxiliary function determined by V. In this paper, the authors characterize the localized Hardy spaces \(H^1_\rho({{\mathbb R}^n})\) in terms of localized Riesz transforms and establish the boundedness on the BMO-type space \({\mathop\mathrm{BMO_\rho({\mathbb R}^n)}}\) of these operators as well as the boundedness from \({\mathop\mathrm{BMO_\rho({\mathbb R}^n)}}\) to \({\mathop\mathrm{BLO_\rho({\mathbb R}^n)}}\) of their corresponding maximal operators, and as a consequence, the authors obtain the Fefferman–Stein decomposition of \({\mathop\mathrm{BMO_\rho({\mathbb R}^n)}}\) via localized Riesz transforms. When ρ is the known auxiliary function determined by V, \({\mathop\mathrm{BMO_\rho({\mathbb R}^n)}}\) is just the known space \(\mathop\mathrm{BMO}_{\mathcal L}({{\mathbb R}^n})\), and \({\mathop\mathrm{BLO_\rho({\mathbb R}^n)}}\) in this case is correspondingly denoted by \(\mathop\mathrm{BLO}_{\mathcal L}({{\mathbb R}^n})\). As applications, when n?≥?3, the authors further obtain the boundedness on \(\mathop\mathrm{BMO}_{\mathcal L}({{\mathbb R}^n})\) of Riesz transforms \(\nabla{\mathcal L}^{-1/2}\) and their adjoint operators, as well as the boundedness from \(\mathop\mathrm{BMO}_{\mathcal L}({{\mathbb R}^n})\) to \(\mathop\mathrm{BLO}_{\mathcal L}({{\mathbb R}^n})\) of their maximal operators. Also, some endpoint estimates of fractional integrals associated to \({\mathcal L}\) are presented. 相似文献
5.
We provide a categorification of \(\mathfrak {q}(2)\)-crystals on the singular \(\mathfrak {gl}_{n}\)-category \({\mathcal O}_{n}\). Our result extends the \(\mathfrak {gl}_{2}\)-crystal structure on \(\text {Irr} ({\mathcal O}_{n})\) induced from the work of Bernstein-Frenkel-Khovanov. Further properties of the \({\mathfrak q}(2)\)-crystal \(\text {Irr} ({\mathcal O}_{n})\) are also discussed. 相似文献
6.
Let \({\mathcal {M}}_{mn}={\mathcal {M}}_{mn}({\mathbb {F}})\) denote the set of all \(m\times n\) matrices over a field \({\mathbb {F}}\), and fix some \(n\times m\) matrix \(A\in {\mathcal {M}}_{nm}\). An associative operation \(\star \) may be defined on \({\mathcal {M}}_{mn}\) by \(X\star Y=XAY\) for all \(X,Y\in {\mathcal {M}}_{mn}\), and the resulting sandwich semigroup is denoted \({\mathcal {M}}_{mn}^A={\mathcal {M}}_{mn}^A({\mathbb {F}})\). These semigroups are closely related to Munn rings, which are fundamental tools in the representation theory of finite semigroups. We study \({\mathcal {M}}_{mn}^A\) as well as its subsemigroups \(\hbox {Reg}({\mathcal {M}}_{mn}^A)\) and \({\mathcal {E}}_{mn}^A\) (consisting of all regular elements and products of idempotents, respectively), and the ideals of \(\hbox {Reg}({\mathcal {M}}_{mn}^A)\). Among other results, we characterise the regular elements; determine Green’s relations and preorders; calculate the minimal number of matrices (or idempotent matrices, if applicable) required to generate each semigroup we consider; and classify the isomorphisms between finite sandwich semigroups \({\mathcal {M}}_{mn}^A({\mathbb {F}}_1)\) and \({\mathcal {M}}_{kl}^B({\mathbb {F}}_2)\). Along the way, we develop a general theory of sandwich semigroups in a suitably defined class of partial semigroups related to Ehresmann-style “arrows only” categories; we hope this framework will be useful in studies of sandwich semigroups in other categories. We note that all our results have applications to the variants \({\mathcal {M}}_n^A\) of the full linear monoid \({\mathcal {M}}_n\) (in the case \(m=n\)), and to certain semigroups of linear transformations of restricted range or kernel (in the case that \(\hbox {rank}(A)\) is equal to one of m, n). 相似文献
7.
V. Adamyan H. Langer C. Tretter M. Winklmeier 《Integral Equations and Operator Theory》2016,84(1):121-149
Suppose that \({\mathcal {M}}\) is a countably decomposable type II\({_1}\) von Neumann algebra and \({\mathcal {A}}\) is a separable, non-nuclear, unital C\({^*}\)-algebra. We show that, if \({\mathcal {M}}\) has Property \({\Gamma}\), then the similarity degree of \({\mathcal {M}}\) is less than or equal to 5. If \({\mathcal {A}}\) has Property c\({^*}\)-\({\Gamma}\), then the similarity degree of \({\mathcal {A}}\) is equal to 3. In particular, the similarity degree of a \({\mathcal {Z}}\)-stable, separable, non-nuclear, unital C\({^*}\)-algebra is equal to 3. 相似文献
8.
A functional distance \({\mathbb H}\), based on the Hausdorff metric between the function hypographs, is proposed for the space \({\mathcal E}\) of non-negative real upper semicontinuous functions on a compact interval. The main goal of the paper is to show that the space \(({\mathcal E},{\mathbb H})\) is particularly suitable in some statistical problems with functional data which involve functions with very wiggly graphs and narrow, sharp peaks. A typical example is given by spectrograms, either obtained by magnetic resonance or by mass spectrometry. On the theoretical side, we show that \(({\mathcal E},{\mathbb H})\) is a complete, separable locally compact space and that the \({\mathbb H}\)-convergence of a sequence of functions implies the convergence of the respective maximum values of these functions. The probabilistic and statistical implications of these results are discussed, in particular regarding the consistency of k-NN classifiers for supervised classification problems with functional data in \({\mathbb H}\). On the practical side, we provide the results of a small simulation study and check also the performance of our method in two real data problems of supervised classification involving mass spectra. 相似文献
9.
Sadek Al Harbat 《Journal of Algebraic Combinatorics》2017,45(3):803-824
We define a tower of injections of \(\tilde{C}\)-type Coxeter groups \(W({\tilde{C}}_{n})\) for \(n\ge 1\). We define a tower of Hecke algebras, and we use the faithfulness at the Coxeter level to show that this last tower is a tower of injections. Let \(W^c({\tilde{C}}_{n})\) be the set of fully commutative elements in \(W({\tilde{C}}_{n})\), we classify the elements of \(W^c({\tilde{C}}_{n})\) and give a normal form for them. We use this normal form to define two injections from \(W^c({\tilde{C}}_{n-1})\) into \(W^c({\tilde{C}}_{n})\). We then define the tower of affine Temperley–Lieb algebras of type \(\tilde{C }\) and use the injections above to prove the faithfulness of this tower. 相似文献
10.
The moduli space \({\mathcal {M}}_{g}\), of genus \(g\ge 2\) closed Riemann surfaces, is a complex orbifold of dimension \(3(g-1)\) which carries a natural real structure, i.e. it admits an anti-holomorphic involution \(\sigma \). The involution \(\sigma \) maps each point corresponding to a Riemann surface S to its complex conjugate \(\overline{S}\). The fixed point set of \(\sigma \) consists of the isomorphism classes of closed Riemann surfaces admitting an anticonformal automorphism. Inside \(\mathrm {Fix}(\sigma )\) is the locus \({\mathcal {M}}_{g}(\mathbb {R})\), the set of real Riemann surfaces, which is known to be connected by results due to P. Buser, M. Seppälä, and R. Silhol. The complement \(\mathrm {Fix}(\sigma )-{\mathcal {M}}_{g}(\mathbb {R})\) consists of the so called pseudo-real Riemann surfaces, which is known to be non-connected. In this short note we provide a simple argument to observe that \(\mathrm {Fix}(\sigma )\) is connected. 相似文献
11.
For a commutative C*-algebra \({\mathcal {A}}\) with unit e and a Hilbert \({\mathcal {A}}\)-module \({\mathcal {M}}\), denote by End\(_{{\mathcal {A}}}({\mathcal {M}})\) the algebra of all bounded \({\mathcal {A}}\)-linear mappings on \({\mathcal {M}}\), and by End\(^*_{{\mathcal {A}}}({\mathcal {M}})\) the algebra of all adjointable mappings on \({\mathcal {M}}\). We prove that if \({\mathcal {M}}\) is full, then each derivation on End\(_{{\mathcal {A}}}({\mathcal {M}})\) is \({\mathcal {A}}\)-linear, continuous, and inner, and each 2-local derivation on End\(_{{\mathcal {A}}}({\mathcal {M}})\) or End\(^{*}_{{\mathcal {A}}}({\mathcal {M}})\) is a derivation. If there exist \(x_0\) in \({\mathcal {M}}\) and \(f_0\) in \({\mathcal {M}}^{'}\), such that \(f_0(x_0)=e\), where \({\mathcal {M}}^{'}\) denotes the set of all bounded \({\mathcal {A}}\)-linear mappings from \({\mathcal {M}}\) to \({\mathcal {A}}\), then each \({\mathcal {A}}\)-linear local derivation on End\(_{{\mathcal {A}}}({\mathcal {M}})\) is a derivation. 相似文献
12.
In this paper we investigate the existence of “partially” isometric immersions. These are maps \({f:M\rightarrow \mathbb{R}^q}\) which, for a given Riemannian manifold M, are isometries on some sub-bundle \({\mathcal{H}\subset TM}\). The concept of free maps, which is essential in the Nash–Gromov theory of isometric immersions, is replaced here by that of \({\mathcal{H}}\) –free maps, i.e. maps whose restriction to \({\mathcal{H}}\) is free. We prove, under suitable conditions on the dimension q of the Euclidean space, that \({\mathcal{H}}\) –free maps are generic and we provide, for the smallest possible value of q, explicit expressions for \({\mathcal{H}}\) –free maps in the following three settings: 1–dimensional distributions in \({\mathbb{R}^2}\), Lagrangian distributions of completely integrable systems, Hamiltonian distributions of a particular kind of Poisson Bracket. 相似文献
13.
M. Petrich 《Acta Mathematica Hungarica》2016,148(2):328-359
As a generalization of completely regular semigroups, which can be written as \({\mathcal{(G \circ RB) \circ S}}\) where \({\mathcal{G}}\), \({\mathcal{RB}}\) and \({\mathcal S}\) are the varieties of groups, rectangular bands and semilattices, respectively, we have replaced \({\mathcal G}\) by the class \({\mathcal M}\) of monoids. This calls for finding the structure of such semigroups, and, as a first step, characterizations. 相似文献
14.
Lauren B. M. Sager 《Integral Equations and Operator Theory》2016,86(3):377-407
We prove a Beurling-Blecher-Labuschagne theorem for \({H^\infty}\)-invariant spaces of \({L^p(\mathcal{M},\tau)}\) when \({0 < p \leq\infty}\), using Arveson’s non-commutative Hardy space \({H^\infty}\) in relation to a von Neumann algebra \({\mathcal{M}}\) with a semifinite, faithful, normal tracial weight \({\tau}\). Using the main result, we are able to completely characterize all \({H^\infty}\)-invariant subspaces of \({L^p(\mathcal{M} \rtimes_\alpha \mathbb{Z},\tau)}\), where \({\mathcal{M} \rtimes_\alpha \mathbb{Z} }\) is a crossed product of a semifinite von Neumann algebra \({\mathcal{M}}\) by the integer group \({\mathbb{Z}}\), and \({H^\infty}\) is a non-selfadjoint crossed product of \({\mathcal{M}}\) by \({\mathbb{Z}^+}\). As an example, we characterize all \({H^\infty}\)-invariant subspaces of the Schatten p-class \({S^p(\mathcal{H})}\), where \({H^\infty}\) is the lower triangular subalgebra of \({B(\mathcal{H})}\), for each \({0 < p \leq\infty}\). 相似文献
15.
Let \(\mathcal {R}\) be a prime ring, \(\mathcal {Z(R)}\) its center, \(\mathcal {C}\) its extended centroid, \(\mathcal {L}\) a Lie ideal of \(\mathcal {R}, \mathcal {F}\) a generalized skew derivation associated with a skew derivation d and automorphism \(\alpha \). Assume that there exist \(t\ge 1\) and \(m,n\ge 0\) fixed integers such that \( vu = u^m\mathcal {F}(uv)^tu^n\) for all \(u,v \in \mathcal {L}\). Then it is shown that either \(\mathcal {L}\) is central or \(\mathrm{char}(\mathcal {R})=2, \mathcal {R}\subseteq \mathcal {M}_2(\mathcal {C})\), the ring of \(2\times 2\) matrices over \(\mathcal {C}, \mathcal {L}\) is commutative and \(u^2\in \mathcal {Z(R)}\), for all \(u\in \mathcal {L}\). In particular, if \(\mathcal {L}=[\mathcal {R,R}]\), then \(\mathcal {R}\) is commutative. 相似文献
16.
Jerome Galtier 《Annals of Operations Research》2018,271(2):575-598
We study packing problems with matroid structures, which includes the strength of a graph of Cunningham and scheduling problems. If \(\mathcal {M}\) is a matroid over a set of elements S with independent set \(\mathcal {I}\), and \(m=|S|\), we suppose that we are given an oracle function that takes an independent set \(A\in \mathcal {I}\) and an element \(e\in S\) and determines if \(A\cup \{e\}\) is independent in time I(m). Also, given that the elements of A are represented in an ordered way \(A=\{A_1,\dots ,A_k\}\), we denote the time to check if \(A\cup \{e\}\notin \mathcal {I}\) and if so, to find the minimum \(i\in \{0,\dots ,k\}\) such that \(\{A_1,\dots ,A_i\}\cup \{e\}\notin \mathcal {I}\) by \(I^*(m)\). Then, we describe a new FPTAS that computes for any \(\varepsilon >0\) and for any matroid \(\mathcal {M}\) of rank r over a set S of m elements, in memory space O(m), the packing \(\varLambda ({\mathcal {M}})\) within \(1+\varepsilon \) in time \(O(mI^*(m)\log (m)\log (m/r)/\varepsilon ^2)\), and the covering \(\varUpsilon ({\mathcal {M}})\) in time \(O(r\varUpsilon ({\mathcal {M}})I(m)\log (m)\log (m/r)/\varepsilon ^2)\). This method outperforms in time complexity by a factor of \(\varOmega (m/r)\) the FPTAS of Plotkin, Shmoys, and Tardos, and a factor of \(\varOmega (m)\) the FPTAS of Garg and Konemann. On top of the value of the packing and the covering, our algorithm exhibits a combinatorial object that proves the approximation. The applications of this result include graph partitioning, minimum cuts, VLSI computing, job scheduling and others. 相似文献
17.
Seok-Jin Kang Masaki Kashiwara Myungho Kim Se-Jin Oh 《Selecta Mathematica, New Series》2016,22(4):1987-2015
Let \(U'_q(\mathfrak {g})\) be a twisted affine quantum group of type \(A_{N}^{(2)}\) or \(D_{N}^{(2)}\) and let \(\mathfrak {g}_{0}\) be the finite-dimensional simple Lie algebra of type \(A_{N}\) or \(D_{N}\). For a Dynkin quiver of type \(\mathfrak {g}_{0}\), we define a full subcategory \({\mathcal C}_{Q}^{(2)}\) of the category of finite-dimensional integrable \(U'_q(\mathfrak {g})\)-modules, a twisted version of the category \({\mathcal C}^{(1)}_{Q}\) introduced by Hernandez and Leclerc. Applying the general scheme of affine Schur–Weyl duality, we construct an exact faithful KLR-type duality functor \({\mathcal F}_{Q}^{(2)}:\mathrm{Rep}(R) \rightarrow {\mathcal C}_{Q}^{(2)}\), where \(\mathrm{Rep}(R)\) is the category of finite-dimensional modules over the quiver Hecke algebra R of type \(\mathfrak {g}_{0}\) with nilpotent actions of the generators \(x_k\). We show that \({\mathcal F}_{Q}^{(2)}\) sends any simple object to a simple object and induces a ring isomorphism Open image in new window . 相似文献
18.
Let \(G=G(k)\) be a connected reductive group over a p-adic field k. The smooth (and tempered) complex representations of G can be considered as the nondegenerate modules over the Hecke algebra \({\mathcal {H}}={\mathcal {H}}(G)\) and the Schwartz algebra \({\mathcal {S}}={\mathcal {S}}(G)\) forming abelian categories \({\mathcal {M}}(G)\) and \({\mathcal {M}}^t(G)\), respectively. Idempotents \(e\in {\mathcal {H}}\) or \({\mathcal {S}}\) define full subcategories \({\mathcal {M}}_e(G)= \{V : {\mathcal {H}}eV=V\}\) and \({\mathcal {M}}_e^t(G)= \{V : {\mathcal {S}}eV=V\}\). Such an e is said to be special (in \({\mathcal {H}}\) or \({\mathcal {S}}\)) if the corresponding subcategory is abelian. Parallel to Bernstein’s result for \(e\in {\mathcal {H}}\) we will prove that, for special \(e \in {\mathcal {S}}\), \({\mathcal {M}}_e^t(G) = \prod _{\Theta \in \theta _e} {\mathcal {M}}^t(\Theta )\) is a finite direct product of component categories \({\mathcal {M}}^t(\Theta )\), now referring to connected components of the center of \({\mathcal {S}}\). A special \(e\in {\mathcal {H}}\) will be also special in \({\mathcal {S}}\), but idempotents \(e\in {\mathcal {H}}\) not being special can become special in \({\mathcal {S}}\). To obtain conditions we consider the sets \(\mathrm{Irr}^t(G) \subset \mathrm{Irr}(G)\) of (tempered) smooth irreducible representations of G, and we view \(\mathrm{Irr}(G)\) as a topological space for the Jacobson topology defined by the algebra \({\mathcal {H}}\). We use this topology to introduce a preorder on the connected components of \(\mathrm{Irr}^t(G)\). Then we prove that, for an idempotent \(e \in {\mathcal {H}}\) which becomes special in \({\mathcal {S}}\), its support \(\theta _e\) must be saturated with respect to that preorder. We further analyze the above decomposition of \({\mathcal {M}}_e^t(G)\) in the case where G is k-split with connected center and where \(e = e_J \in {\mathcal {H}}\) is the Iwahori idempotent. Here we can use work of Kazhdan and Lusztig to relate our preorder on the support \(\theta _{e_J}\) to the reverse of the natural partial order on the unipotent classes in G. We finish by explicitly computing the case \(G=GL_n\), where \(\theta _{e_J}\) identifies with the set of partitions of n. Surprisingly our preorder (which is a partial order now) is strictly coarser than the reverse of the dominance order on partitions. 相似文献
19.
Let \({\mathcal{R}}\) be a unital commutative ring and \({\mathcal{M}}\) be a 2-torsion free central \({\mathcal{R}}\) -bimodule. In this paper, for \({n \geqq 3}\), we show that every local derivation from M n (\({\mathcal{R}}\)) into M n (\({\mathcal{M}}\)) is a derivation. 相似文献
20.
M. Petrich 《Acta Mathematica Hungarica》2018,154(2):429-456
The class \({\mathcal{CR}}\) of completely regular semigroups equipped with the unary operation of inversion forms a variety whose lattice of subvarieties is denoted by \({\mathcal{L(CR)}}\). The variety \({\mathcal B}\) of all bands induces two relations \({\mathbf{B}^{\land}}\) and \({\mathbf{B}^{\lor} }\) by meet and join with \({\mathcal B}\). Their classes are intervals with lower ends \({\mathcal V_{B^{\land}}}\) and \({\mathcal V_{B^{\lor}}}\), and upper ends \({\mathcal V^{B^{\land}}}\) and \({\mathcal V^{B^{\lor}}}\). These objects induce four operators on \({\mathcal{L(CR)}}\).The cluster at a variety \({\mathcal V}\) is the set of all varieties obtained from \({\mathcal V}\) by repeated application of these four operators. We identify the cluster at any variety in \({\mathcal{L(CR)}}\). 相似文献