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A Panorama of Modern Operator Theory and Related Topics

Part of the Operator Theory: Advances and Applications Book Series (volume 218)

Editors: Dym, Harry; Kaashoek, Marinus A.; Lancaster, Peter; Langer, Heinz; Lerer, Leonid

DOI: 10.1007/978-3-0348-0221-5

ISBN: 978-3-0348-0220-8

Publisher: Springer Basel - Springer Journals

Jan 3, 2012

1 - 10 of 27 Chapters

LitStream

Chapter 1An Interpolation Problem for Functions with Values in a Commutative Ring

Alpay, Daniel; Attia, Haim

Pages: 1 –17

[It was recently shown that the theory of linear stochastic systems can be viewed as a particular case of the theory of linear systems on a certain commutative ring of power series in a countable number of variables. In the present work we study an interpolation problem in this setting. A key...
LitStream

Chapter 2Minimal and Maximal Invariant Spaces of Holomorphic Functions on Bounded Symmetric Domains

Arazy, Jonathan; Upmeier, Harald

Pages: 19 –49

[Let D be a Cartan domain in Cd and let G = Aut(D) be the group of all biholomorphic automorphisms of G. Consider the projective representation of G on spaces of holomorphic functions on D ((Uv(g)f)(z){j(g-1))((z))) {j(g -1)(z)}(z)(1())g∈G where z is the genus of D and W is in the Wallach set D....
LitStream

Chapter 3B-regular J-inner Matrix-valued Functions

Arov, Damir Z.; Dym, Harry

Pages: 51 –73

[In the study of the class U((j)) of mvf’s (matrix-valued functions) that are ??-inner with respect to the open upper half-plane C+ and a given signature matrix j, special roles are played by the classes uer((j)), (j)(Ur), UrR((j)) and () of left regular, right regular, left strongly regular and...
LitStream

Chapter 4Canonical Transfer-function Realization for Schur-Agler-class Functions of the Polydisk

Ball, Joseph A.; Bolotnikov, Vladimir

Pages: 75 –122

[Associated with any Schur-class function S((z)) (i.e., a contractive operator-valued holomorphic function on the unit disk) is the de Branges- Rovnyak kernel Ks((z,C)) = [=([I-S(z))S(C)) * ]/(1–) and the reproducing kernel Hilbert space H(KS) which serves as the canonical functional-model...
LitStream

Chapter 5Spectral Regularity of Banach Algebras and Non-commutative Gelfand Theory

Bart, Harm; Ehrhardt, Torsten; Silbermann, Bernd

Pages: 123 –153

[A new non-commutative Gelfand type criterion for spectrally regular behavior of vector-valued analytic functions is developed. Applications are given in situations that could not be handled with earlier methods. Some open problems are identified.]
LitStream

Chapter 6Banach Algebras of Commuting Toeplitz Operators on the Unit Ball via the Quasi-hyperbolic Group

Bauer, Wolfram; Vasilevski, Nikolai

Pages: 155 –175

[We continue the study of commutative algebras generated by Toeplitz operators acting on the weighted Bergman spaces over the unit ball Bn in Cn. As was observed recently, apart of the already known commutative Toeplitz C * -algebras, quite unexpectedly, there exist many others, not geometrically...
LitStream

Chapter 7Canonical Models for Bi-isometries

Bercovici, H.; Douglas, R. G.; Foias, C.

Pages: 177 –205

[A canonical model, analogous to the one for contraction operators, is introduced for bi-isometries, two commuting isometries on a Hilbert space. This model involves a contractive analytic operator-valued function on the unit disk. Various complete nonunitarity conditions are considered as well...
LitStream

Chapter 8First-order Trace Formulae for the Iterates of the Fox–Li Operator

Böttcher, Albrecht; Grudsky, Sergei; Huybrechs, Daan; Iserles, Arieh

Pages: 207 –224

[The paper is devoted to first-order trace formulas for the iterates of the Fox–Li and related Wiener–Hopf integral operators. Such formulas provide first insight into the asymptotic behaviour of the eigenvalues and can be used to test whether a specific guess for the eigenvalue distribution is...
LitStream

Chapter 9Factorization Versus Invertibility of Matrix Functions on Compact Abelian Groups

Brudnyi, Alex; Rodman, Leiba; Spitkovsky, Ilya M.

Pages: 225 –239

[Open problems are stated and some new results are proved concerning the relationship between invertibility and factorization in various Banach algebras of matrix-valued functions on connected compact abelian groups.]
LitStream

Chapter 10Banded Matrices, Banded Inverses and Polynomial Representations for Semi-separable Operators

Dewilde, Patrick

Pages: 241 –268

[The paper starts out with exploring properties of the URV factorization in the case of banded matrices or operators with banded inverse, showing that they result in factors with the same properties. Then it gives a derivation of representations for general semi-separable operators (matrices) as...

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