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1.
Let Γ be a countable group and denote by S{\mathcal{S}} the equivalence relation induced by the Bernoulli action
G\curvearrowright [0, 1]G{\Gamma\curvearrowright [0, 1]^{\Gamma}}, where [0, 1]Γ is endowed with the product Lebesgue measure. We prove that, for any subequivalence relation R{\mathcal{R}} of S{\mathcal{S}}, there exists a partition {X
i
}
i≥0 of [0, 1]Γ into R{\mathcal{R}}-invariant measurable sets such that R|X0{\mathcal{R}_{\vert X_{0}}} is hyperfinite and R|Xi{\mathcal{R}_{\vert X_{i}}} is strongly ergodic (hence ergodic and non-hyperfinite), for every i ≥ 1. 相似文献
2.
A. Ballester-Bolinches John Cossey R. Esteban-Romero 《Annali di Matematica Pura ed Applicata》2010,189(4):567-570
For a finite group G we define the graph Γ(G) to be the graph whose vertices are the conjugacy classes of cyclic subgroups of G and two conjugacy classes ${\mathcal {A}, \mathcal {B}}For a finite group G we define the graph Γ(G) to be the graph whose vertices are the conjugacy classes of cyclic subgroups of G and two conjugacy classes A, B{\mathcal {A}, \mathcal {B}} are joined by an edge if for some A ? A, B ? B A{A \in \mathcal {A},\, B \in \mathcal {B}\, A} and B permute. We characterise those groups G for which Γ(G) is complete. 相似文献
3.
Esteban Andruchow Jorge Antezana Gustavo Corach 《Integral Equations and Operator Theory》2010,67(4):451-466
Given a closed subspace ${\mathcal{S}}Given a closed subspace S{\mathcal{S}} of a Hilbert space H{\mathcal{H}}, we study the sets FS{\mathcal{F}_\mathcal{S}} of pseudo-frames, CFS{\mathcal{C}\mathcal{F}_\mathcal{S}} of commutative pseudo-frames and
\mathfrakXS{\tiny{\mathfrak{X}}_{\mathcal{S}}} of dual frames for S{\mathcal{S}}, via the (well known) one to one correspondence which assigns a pair of operators (F, H) to a frame pair
({fn}n ? \mathbbN,{hn}n ? \mathbbN){(\{f_n\}_{n\in\mathbb{N}},\{h_n\}_{n\in\mathbb{N}})},
F:l2? H, F({cn}n ? \mathbbN )=?n cn fn,F:\ell^2\to\,\mathcal{H}, \quad F\left(\{c_n\}_{n\in\mathbb{N}} \right)=\sum_n c_n f_n, 相似文献
4.
Kengo Matsumoto 《Mathematische Zeitschrift》2010,265(4):735-760
A C*-symbolic dynamical system ${(\mathcal{A}, \rho, \Sigma)}
5.
Let ${\Gamma < {\rm SL}(2, {\mathbb Z})}
6.
Let ${\mathcal {H}_{1}}
7.
In this paper we present new structural information about the multiplier algebra M (A ){\mathcal M (\mathcal A )} of a σ-unital purely infinite simple C*-algebra A{\mathcal {A}}, by characterizing the positive elements A ? M (A ){A\in \mathcal M (\mathcal A )} that are strict sums of projections belonging to A{\mathcal A } . If A ? A{A\not\in \mathcal {A}} and A itself is not a projection, then the necessary and sufficient condition for A to be a strict sum of projections belonging to A{\mathcal {A} } is that ${\|A\| >1 }${\|A\| >1 } and that the essential norm ||A||ess 3 1{\|A\|_{ess} \geq 1}. Based on a generalization of the Perera–Rordam weak divisibility of separable simple C*-algebras of real rank zero to all σ-unital simple C*-algebras of real rank zero, we show that every positive element of A{\mathcal {A}} with norm >1 can be approximated by finite sums of projections. Based on block tri-diagonal approximations, we decompose
any positive element A ? M (A ){A\in \mathcal M (\mathcal {A} )} with ${\| A\| >1 }${\| A\| >1 } and || A||ess 3 1{\| A\|_{ess} \geq 1} into a strictly converging sum of positive elements in A{\mathcal A} with norm >1. 相似文献
8.
Igor V. Protasov 《Algebra Universalis》2009,62(4):339-343
Let ${\mathbb{A}}
9.
We construct an explicit intertwining operator L{\mathcal L} between the Schr?dinger group eit \frac\triangle2{e^{it \frac\triangle2}} and the geodesic flow on certain Hilbert spaces of symbols on the cotangent bundle T*X Γ of a compact hyperbolic surface X Γ = Γ\D. We also define Γ-invariant eigendistributions of the geodesic flow PSj, k, nj,-nk{PS_{j, k, \nu_j,-\nu_k}} (Patterson-Sullivan distributions) out of pairs of \triangle{\triangle} -eigenfunctions, generalizing the diagonal case j = k treated in Anantharaman and Zelditch (Ann. Henri Poincaré 8(2):361–426, 2007). The operator L{\mathcal L} maps PSj, k, nj,-nk{PS_{j, k, \nu_j,-\nu_k}} to the Wigner distribution WGj,k{W^{\Gamma}_{j,k}} studied in quantum chaos. We define Hilbert spaces HPS{\mathcal H_{PS}} (whose dual is spanned by {PSj, k, nj,-nk{PS_{j, k, \nu_j,-\nu_k}}}), resp. HW{\mathcal H_W} (whose dual is spanned by {WGj,k}{\{W^{\Gamma}_{j,k}\}}), and show that L{\mathcal L} is a unitary isomorphism from HW ? HPS.{\mathcal H_{W} \to \mathcal H_{PS}.} 相似文献
10.
Carlson and Toledo conjectured that if an infinite group Γ is the fundamental group of a compact K?hler manifold, then virtually
H2(G, \mathbb R) 1 0{H^{2}(\Gamma, {\mathbb R}) \ne 0} . We assume that Γ admits an unbounded reductive rigid linear representation. This representation necessarily comes from
a complex variation of Hodge structure (
\mathbbC{\mathbb{C}} -VHS) on the K?hler manifold. We prove the conjecture under some assumption on the
\mathbbC{\mathbb{C}} -VHS. We also study some related geometric/topological properties of period domains associated to such a
\mathbbC{\mathbb{C}} -VHS. 相似文献
11.
John R. Akeroyd Pratibha G. Ghatage Maria Tjani 《Integral Equations and Operator Theory》2010,68(4):503-517
For any analytic self-map j{\varphi} of {z : |z| < 1} we give four separate conditions, each of which is necessary and sufficient for the composition operator Cj{C_{\varphi}} to be closed-range on the Bloch space B{\mathcal{B}} . Among these conditions are some that appear in the literature, where we provide new proofs. We further show that if Cj{C_{\varphi}} is closed-range on the Bergman space
\mathbbA2{\mathbb{A}^2} , then it is closed-range on B{\mathcal{B}} , but that the converse of this fails with a vengeance. Our analysis involves an extension of the Julia-Carathéodory Theorem. 相似文献
12.
We study the projection p: Md ? Bd{\pi : \mathcal{M}_d \rightarrow \mathcal{B}_d} which sends an affine conjugacy class of polynomial
f : \mathbbC ? \mathbbC{f : \mathbb{C} \rightarrow \mathbb{C}} to the holomorphic conjugacy class of the restriction of f to its basin of infinity. When Bd{\mathcal{B}_d} is equipped with a dynamically natural Gromov–Hausdorff topology, the map π becomes continuous and a homeomorphism on the shift locus. Our main result is that all fibers of π are connected. Consequently, quasiconformal and topological basin-of-infinity conjugacy classes are also connected. The key
ingredient in the proof is an analysis of model surfaces and model maps, branched covers between translation surfaces which
model the local behavior of a polynomial. 相似文献
13.
Francesco Polizzi 《Geometriae Dedicata》2010,147(1):323-355
In this paper we investigate the numerical properties of relatively minimal isotrivial fibrations j: X ? C{\varphi : X \longrightarrow C}, where X is a smooth, projective surface and C is a curve. In particular we prove that, if g(C) ≥ 1 and X is neither ruled nor isomorphic to a quasi-bundle, then KX2 £ 8 c(OX)-2{K_X^2 \leq 8 \chi(\mathcal{O}_X)-2} ; this inequality is sharp and if equality holds then X is a minimal surface of general type whose canonical model has precisely two ordinary double points as singularities. Under
the further assumption that K
X
is ample, we obtain KX2 £ 8c(OX)-5{K_X^2 \leq 8\chi(\mathcal{O}_X)-5} and the inequality is also sharp. This improves previous results of Serrano and Tan. 相似文献
14.
Kate Juschenko 《Mathematische Zeitschrift》2010,266(3):693-705
In this paper, we consider ideals of a C
*-algebra C*(B){C^*(\mathcal{B})} generated by an operator algebra B{\mathcal{B}} . A closed ideal J í C*(B){J\subseteq C^*(\mathcal{B})} is called a K-boundary ideal if the restriction of the quotient map on B{\mathcal{B}} has a completely bounded inverse with cb-norm equal to K
−1. For K = 1 one gets the notion of boundary ideals introduced by Arveson. We study properties of the K-boundary ideals and characterize them in the case when operator algebra λ-norms itself. Several reformulations of the Kadison
similarity problem are given. In particular, the affirmative answer to this problem is equivalent to the statement that every
bounded homomorphism from C*(B){C^*(\mathcal{B})} onto B{\mathcal{B}} which is a projection on B{\mathcal{B}} is completely bounded. Moreover, we prove that Kadison’s similarity problem is decided on one particular C
*-algebra which is a completion of the *-double of
M2(\mathbbC){M_2(\mathbb{C})} . 相似文献
15.
Josef Dalík 《Numerische Mathematik》2010,116(4):619-644
For a shape-regular triangulation ${\mathcal{T}_h}
16.
Let H be a multigraph, possibly containing loops. An H-subdivision is any simple graph obtained by replacing the edges of H with paths of arbitrary length. Let H be an arbitrary multigraph of order k, size m, n
0(H) isolated vertices and n
1(H) vertices of degree one. In Gould and Whalen (Graphs Comb. 23:165–182, 2007) it was shown that if G is a simple graph of order n containing an H-subdivision H{\mathcal{H}} and
d(G) 3 \fracn+m-k+n1(H)+2n0(H)2{\delta(G) \ge \frac{n+m-k+n_1(H)+2n_0(H)}{2}}, then G contains a spanning H-subdivision with the same ground set as H{\mathcal{H}} . As a corollary to this result, the authors were able to obtain Dirac’s famed theorem on hamiltonian graphs; namely that
if G is a graph of order n ≥ 3 with
d(G) 3 \fracn2{\delta(G)\ge\frac{n}{2}} , then G is hamiltonian. Bondy (J. Comb. Theory Ser. B 11:80–84, 1971) extended Dirac’s theorem by showing that if G satisfied the condition
d(G) 3 \fracn2{\delta(G) \ge \frac{n}{2}} then G was either pancyclic or a complete bipartite graph. In this paper, we extend the result from Gould and Whalen (Graphs Comb.
23:165–182, 2007) in a similar manner. An H-subdivision H{\mathcal{H}} in G is 1-extendible if there exists an H-subdivision H*{\mathcal{H}^{*}} with the same ground set as H{\mathcal{H}} and |H*| = |H| + 1{|\mathcal{H}^{*}| = |\mathcal{H}| + 1} . If every H-subdivision in G is 1-extendible, then G is pan-H-linked. We demonstrate that if H is sufficiently dense and G is a graph of large enough order n such that
d(G) 3 \fracn+m-k+n1(H)+2n0(H)2{\delta(G) \ge \frac{n+m-k+n_1(H)+2n_0(H)}{2}} , then G is pan-H-linked. This result is sharp. 相似文献
17.
In 1986, the second author classified the minimal clones on a finite universe into five types. We extend this classification to infinite universes and to multiclones. We show that every non-trivial clone contains a “small” clone of one of the five types. From it we deduce, in part, an earlier result, namely that if ${\mathcal{C}}
18.
Martin Reiris 《Annales Henri Poincare》2010,10(8):1559-1604
Let (g, K)(k) be a CMC (vacuum) Einstein flow over a compact three-manifold Σ with non-positive Yamabe invariant (Y(Σ)). As noted by Fischer and Moncrief, the reduced volume ${\mathcal{V}(k)=\left(\frac{-k}{3}\right)^{3}{\rm Vol}_{g(k)}(\Sigma)}
19.
The secant map of an immersion sends a pair of points to the direction of the line joining the images of the points under the immersion. The germ of the secant map of a generic codimension-c immersion $X\!\!:{\mathbb R}^n \to {\mathbb R}^{n+c}
20.
Christophe Dupont 《Mathematische Annalen》2011,349(3):509-528
Let f be an endomorphism of
\mathbbC\mathbbPk{\mathbb{C}\mathbb{P}^k} and ν be an f-invariant measure with positive Lyapunov exponents (λ
1, . . . , λ
k
). We prove a lower bound for the pointwise dimension of ν in terms of the degree of f, the exponents of ν and the entropy of ν. In particular our result can be applied for the maximal entropy measure μ. When k = 2, it implies that the Hausdorff dimension of μ is estimated by dimHm 3 [(log d)/(l1)] + [(log d)/(l2)]{{\rm dim}_\mathcal{H}\mu \geq {{\rm log} d \over \lambda_1} + {{\rm log} d \over \lambda_2}}, which is half of the conjectured formula. Our method for proving these results consists in studying the distribution of
the ν-generic inverse branches of f
n
in
\mathbbC\mathbbPk{\mathbb{C}\mathbb{P}^k} . Our tools are a volume growth estimate for the bounded holomorphic polydiscs in
\mathbbC\mathbbPk{\mathbb{C}\mathbb{P}^k} and a normalization theorem for the ν-generic inverse branches of f
n
. 相似文献
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