Algebraic Methods in Operator Theory

✍ Scribed by Radu Gadidov (auth.), Raúl E. Curto, Palle E. T. Jørgensen (eds.)

• Publisher: Birkhäuser Basel
• Year: 1994
• Tongue: English
• Leaves: 359
• Edition: 1
• Category: Library

✦ Synopsis

The theory of operators stands at the intersection of the frontiers of modern analysis and its classical counterparts; of algebra and quantum mechanics; of spectral theory and partial differential equations; of the modern global approach to topology and geometry; of representation theory and harmonic analysis; and of dynamical systems and mathematical physics. The present collection of papers represents contributions to a conference, and they have been carefully selected with a view to bridging different but related areas of mathematics which have only recently displayed an unexpected network of interconnections, as well as new and exciting cross-fertilizations. Our unify­ ing theme is the algebraic view and approach to the study of operators and their applications. The complementarity between the diversity of topics on the one hand and the unity of ideas on the other has been stressed. Some of the longer contributions represent material from lectures (in expanded form and with proofs for the most part). However, the shorter papers, as well as the longer ones, are an integral part of the picture; they have all been carefully refereed and revised with a view to a unity of purpose, timeliness, readability, and broad appeal. Raul Curto and Paile E. T.

✦ Table of Contents

Front Matter....Pages i-viii
Front Matter....Pages 1-1
On the Commutant Lifting Theorem and Hankel Operators....Pages 3-9
Operator Semigroups, Invariant Sets and Invariant Subspaces....Pages 10-14
The Local de Branges-Rovnyak Construction and Complete Nevanlinna-Pick Kernels....Pages 15-24
Local Spectral Theory for Multipliers and Convolution Operators....Pages 25-36
Operator-Valued Poisson Kernels and Standard Models in Several Variables....Pages 37-46
Front Matter....Pages 47-47
Elementary operators and subalgebras....Pages 49-51
Questions on Bimodules of Nest Algebras....Pages 52-58
The Universal Factorization Property for Commutative Subspace Lattices....Pages 59-65
Compression Limit Algebras....Pages 66-78
Inverse Semigroups, Groupoids and A Problem of J. Renault....Pages 79-89
On Banach Algebras Generated by Two Idempotents....Pages 90-97
Front Matter....Pages 99-99
Berezin-Toeplitz Quantization....Pages 101-108
Normal Elements of a Simple C-Algebra....Pages 109-123
A Gelfand-Naimark Theorem for C-Algebras....Pages 124-133
The Generalized Weyl-von Neumann Theorem and C-algebra Extensions....Pages 134-143
The cb -norm of a derivation....Pages 144-152
Hopf C -Algebras And Their Representations....Pages 153-162
Quasi-Diagonalizing Unitaries and the Generalized Weyl-Von Neumann Theorem....Pages 163-171
Front Matter....Pages 173-173
On the Structure of Finite Depth Subfactors....Pages 175-194
Universally bounded operators on von Neumann algebras of type II 1 ....Pages 195-204
Front Matter....Pages 173-173
Non occurrence of star graphs as principal graphs....Pages 205-217
Depth 2 Subfactors and Hopf Algebra Crossed Products....Pages 218-222
Front Matter....Pages 223-223
Generalized Characters of U ∞....Pages 225-235
Module structures on Hochschild and cyclic cohomology of crossed products....Pages 236-260
q -Relations and Stability of C-Isomorphism Classes....Pages 261-271
A test for injectivity for asymptotic morphisms....Pages 272-275
On the “quantum disk” and a “non-commutative circle”....Pages 276-290
Landstad Duality for Coactions on C -Algebras....Pages 291-295
Quantization of Poisson SU (2)....Pages 296-304
Front Matter....Pages 305-305
“Vector bundles” over quantum Heisenberg manifolds....Pages 307-315
Deformations of topological spaces predicted by E -theory....Pages 316-327
Analyticity, Uniform Averaging and K-Theory....Pages 328-349
Boundary Value Problems for Functions Analytic on Multiply Connected Domains on Spaces with a General Weight....Pages 350-360

✦ Subjects

Operator Theory; Algebra