共查询到20条相似文献,搜索用时 0 毫秒
1.
Xavier Mary 《Integral Equations and Operator Theory》2008,60(3):419-433
We discuss the notion of Moore-Penrose inverse in Kreĭn spaces for both bounded and unbounded operators. Conditions for the
existence of a Moore-Penrose inverse are given. We then investigate its relation with adjoint operators, and study the involutive
Banach algebra . Finally applications to the Schur complement are given.
相似文献
2.
The structure of unitary relations between Kreĭn spaces is investigated in geometrical terms. Two approaches are presented:
The first approach relies on the so-called Weyl identity and the second approach is based on a graph decomposition of unitary
relations. As a consequence of these investigations a quasi-block and a proper block representation of unitary operators are
established. Both approaches yield also several new necessary and sufficient conditions for isometric relations to be unitary. 相似文献
3.
4.
Hankel operators and their symbols, as generalized by V. Pták and P. Vrbová, are considered in the Kreĭn space setting. Under
a generic assumption, without which the Krein space case may be untreatable, a necessary and sufficient condition for the
existence of Hankel symbols for a given Hankel operator X is given. A parametric labeling of the Hankel symbols of X by means of Schur class functions is obtained. The proof is established by associating to the data of the problem an isometry
V acting on a Kreĭn space so that there is a bijective correspondence between the symbols of X and the minimal unitary Hilbert space extensions of V . The result includes uniqueness criteria and a Schur like formula. 相似文献
5.
Uğur Gönüllü 《Archiv der Mathematik》2016,106(1):41-51
We give a representation of cyclically compact self-adjoint operators on Kaplansky–Hilbert modules and characterize the global eigenvalues of such operators by a sequence consisting of their global eigenvalues taken in the corresponding representation. 相似文献
6.
Yury Arlinskiĭ 《Integral Equations and Operator Theory》2011,71(3):417-453
We establish connections between Schur parameters of the Schur class operator-valued functions, the corresponding simple conservative
realizations, lower triangular Toeplitz matrices, and Kreĭn shorted operators. By means of Schur parameters or shorted operators
for defect operators of Toeplitz matrices necessary and sufficient conditions for a simple conservative discrete-time system
to be controllable/observable and for a completely non-unitary contraction to be completely non-isometric/completely non-co-isometric
are obtained. For the Schur problem a characterization of central solution and uniqueness criteria to the solution are given
in terms of shorted operators for defect operators of contractive Toeplitz matrices, corresponding to data. 相似文献
7.
8.
Damir Z. Arov 《Journal of Functional Analysis》2009,256(12):3892-3327
Let Z be a maximal nonnegative subspace of a Kre?n space X, and let X/Z be the quotient of X modulo Z. Define
H(Z)={h∈X/Z|sup{−X[x,x]|x∈h}<∞}. 相似文献
9.
Kun-yu GUO & Peng-hui WANG School of Mathematics Pudan University Shanghai China 《中国科学A辑(英文版)》2007,(3)
In this paper, we study the homogenous quotient modules of the Hardy module on the bidisk. The essential normality of the homogenous quotient modules is completely characterized. We also describe the essential spectrum for a general quotient module. The paper also considers K-homology invariant defined in the case of the homogenous quotient modules on the bidisk. 相似文献
10.
In this paper, we study the homogenous quotient modules of the Hardy module on the bidisk. The essential normality of the
homogenous quotient modules is completely characterized. We also describe the essential spectrum for a general quotient module.
The paper also considers K-homology invariant defined in the case of the homogenous quotient modules on the bidisk.
This work is partially supported by the National Natural Science Foundation of China (Grant No. 10525106), the Young Teacher
Fund, the National Key Basic Research Project of China (Grant No. 2006CB805905) and the Specialized Research for the Doctoral
Program 相似文献
11.
Fang Ainong 《数学学报(英文版)》1993,9(3):231-239
We will solve several fundamental problems of Möbius groupsM(R n) which have been matters of interest such as the conjugate classification, the establishment of a standard form without finding the fixed points and a simple discrimination method. Let \(g = \left[ {\begin{array}{*{20}c} a &; b \\ c &; d \\ \end{array} } \right]\) be a Clifford matrix of dimensionn, c ≠ 0. We give a complete conjugate classification and prove the following necessary and sufficient conditions:g is f.p.f. (fixed points free) iff \(g \sim \left[ {\begin{array}{*{20}c} \alpha &; 0 \\ c &; {\alpha '} \\ \end{array} } \right]\) , |α|<1 and |E?AE 1| ≠ 0;g is elliptic iff \(g \sim \left[ {\begin{array}{*{20}c} \alpha &; \beta \\ c &; {\alpha '} \\ \end{array} } \right]\) , |α| <1 and |E?AE 1|=0;g is parabolic iff \(g \sim \left[ {\begin{array}{*{20}c} \alpha &; 0 \\ c &; {\alpha '} \\ \end{array} } \right]\) , |α|=1; andg is loxodromic iff \(g \sim \left[ {\begin{array}{*{20}c} \alpha &; \beta \\ c &; {\alpha '} \\ \end{array} } \right]\) , |α| >1 or rank (E?AE 1) ≠ rank (E?AE 1,ac ?1+c ?1 d), where α is represented by the solutions of certain linear algebraic equations and satisfies $\left| {c^{ - 1} \alpha '} \right| = \left| {\left( {E - AE^1 } \right)^{ - 1} \left( {\alpha c^{ - 1} + c^{ - 1} \alpha '} \right)} \right|.$ 相似文献
12.
A Kre?n-de Branges-Kotani space $\mathbb{H }$ is associated to a given positive-definite distribution $Q$ on the finite interval $(-a,a)$ of the real line. The Kre?n-de Branges Theorem is applied to get a spectral measure of $\mathbb{H }$ . In this way a simple proof of the solubility of the Kre?n’s extension problem related to $Q$ (Kre?n–Schwartz Theorem) is obtained. A condition that guarantees the uniqueness of the extrapolation as well as a parameterization of the extrapolations by means of Schur functions are given. The choice of the Schur function $\eta \equiv 0$ in the parameterization is shown to produce an absolutely continuous measure which maximizes Burg’s entropy. The results are based on the coupling of the Arov–Grossman functional model with a Hilbert space operator built up from the multiplication operator on $\mathbb{H }$ . 相似文献
13.
Harald Woracek 《Monatshefte für Mathematik》2012,167(1):105-149
A string is a pair \({(L, \mathfrak{m})}\) where \({L \in[0, \infty]}\) and \({\mathfrak{m}}\) is a positive, possibly unbounded, Borel measure supported on [0, L]; we think of L as the length of the string and of \({\mathfrak{m}}\) as its mass density. To each string a differential operator acting in the space \({L^2(\mathfrak{m})}\) is associated. Namely, the Kre?n–Feller differential operator \({-D_{\mathfrak{m}}D_x}\) ; its eigenvalue equation can be written, e.g., asA positive Borel measure τ on \({\mathbb R}\) is called a (canonical) spectral measure of the string \({\textsc S[L, \mathfrak{m}]}\) , if there exists an appropriately normalized Fourier transform of \({L^2(\mathfrak{m})}\) onto L 2(τ). In order that a given positive Borel measure τ is a spectral measure of some string, it is necessary that: (1) \({\int_{\mathbb R} \frac{d\tau(\lambda)}{1+|\lambda|} < \infty}\) . (2) Either \({{\rm supp} \tau \subseteq [0, \infty)}\) , or τ is discrete and has exactly one point mass in (?∞, 0). It is a deep result, going back to Kre?n in the 1950’s, that each measure with \({\int_{\mathbb R}\frac{d\tau(\lambda)}{1+|\lambda|} < \infty}\) and \({{\rm supp} \tau \subseteq [0, \infty)}\) is a spectral measure of some string, and that this string is uniquely determined by τ. The question remained open, which conditions characterize whether a measure τ with \({{\rm supp} \tau \not\subseteq [0, \infty)}\) is a spectral measure of some string. In the present paper, we answer this question. Interestingly, the solution is much more involved than the first guess might suggest.
相似文献
$$f^{\prime}(x) + z \int_0^L f(y)\,d\mathfrak{m}(y) = 0,\quad x \in\mathbb R,\ f^{\prime}(0-) = 0.$$
14.
We present a short and elementary proof of isometric uniqueness of the Gurari? space. 相似文献
15.
We deal with the Kreîn-Langer problem for
-valued functions on the band (–2a, 2a)×, where
is the algebra of continuous linear operators on a Hilbert space
,a a finite positive number and a topological Abelian group. We show that every weakly continuous -indefinite function
admits a strongly continuous -indefinite continuation to × with the same indefiniteness index . We give a parametrization of the extensions in terms of operator-valued Schur functions. 相似文献
16.
The commutant and similarity invariant of analytic Toeplitz operators on Bergman space 总被引:1,自引:0,他引:1
The famous von Neumann-Wold Theorem tells us that each analytic Toeplitz operator with n 1-Blaschke factors is unitary to n 1 copies of the unilateral shift on the Hardy space. It is obvious that the von Neumann-Wold Theorem does not hold in the Bergman space. In this paper, using the basis constructed by Michael and Zhu on the Bergman space we prove that each analytic Toeplitz operator Mb(z) is similar to n 1 copies of the Bergman shift if and only if B(z) is an n 1-Blaschke product. Prom the above theorem, we characterize the similarity invariant of some analytic Toeplitz operators by using K0-group term. 相似文献
17.
18.
19.
Ali Zamani Mohammad Sal Moslehian Mao-Ting Chien Hiroshi Nakazato 《Linear and Multilinear Algebra》2013,61(11):2147-2158
ABSTRACTWe present a necessary and sufficient condition for the norm-parallelism of bounded linear operators on a Hilbert space. We also give a characterization of the Birkhoff–James orthogonality for Hilbert space operators. Moreover, we discuss the connection between norm-parallelism to the identity operator and an equality condition for the Davis–Wielandt radius. Some other related results are also discussed. 相似文献
20.
Hendryk Pfeiffer 《Journal of Algebra》2009,321(12):3714-3763
We show that every modular category is equivalent as an additive ribbon category to the category of finite-dimensional comodules of a Weak Hopf Algebra. This Weak Hopf Algebra is finite-dimensional, split cosemisimple, weakly cofactorizable, coribbon and has trivially intersecting base algebras. In order to arrive at this characterization of modular categories, we develop a generalization of Tannaka–Kre?ˇn reconstruction to the long version of the canonical forgetful functor which is lax and oplax monoidal, but not in general strong monoidal, thereby avoiding all the difficulties related to non-integral Frobenius–Perron dimensions. In the more general case of a finitely semisimple additive ribbon category, not necessarily modular, the reconstructed Weak Hopf Algebra is finite-dimensional, split cosemisimple, coribbon and has trivially intersecting base algebras. 相似文献