Multivariable Operator Theory



Raul E. Curio, Ronald G. Douglas, Joel D. Pincus, Norberto Salinas, "Multivariable Operator Theory"
American Mathematical Society | 1995 | ISBN: 0821802984 | 380 pages | File type: PDF | 6,6 mb

This volume contains a collection of papers presented at the Summer Research Conference on Multivariable Operator Theory, held in July 1993 at the University of Washington in Seattle. The articles contain contributions to a variety of areas and topics which may be viewed as forming an emerging new subject. This subject involves the study of geometric rather than topological invariants associated with the general theme of operator theory in several variables. Developments have occurred in several different directions, with the aid of a variety of techniques, and many advances have been made through cross-pollination among different areas of mathematics. The goal of the conference, and of this volume, is to spur discussion of the connections among the various approaches and new directions for research.
Contents

Explicit formulae for Taylor's functional calculus 1
A survey of invariant Hilbert spaces of analytic functions on bounded symmetric domains 7
Homogeneous operators and systems of imprimitivity 67
Duality between A^\infty and A^{-\infty}on domains with nondegenerate corners 77
Commutative subspace lattices, complete distributivity and approximation 89
Models and resolutions for Hilbert modules 109
Positivity, extensions and the truncated complex moment problem 133
Torsion invariants for finite von Neumann algebras 151
Algebraic K-theory invariants for operator theory 187
Fundamentals of harmonic analysis on domains in complex space 195
Spectral picture and index invariants of commuting n-tuples of operators 219
Schatten class of Hankel and Toeplitz operators on the Bergman space of strongly pseudoconvex domains 237
Operator equations with elementary operators 259
Membership in the Class 273
Hogher Order Kankel Forms 283
Real Valued Spectral Flow 307
Abstract \dbar-resolution for Several Commuting 319
Toeplitz C*-Algebras and Several Complex Variables 339
Positivity Conditions and Standard Models for Commuting Multioperators 347
Trace Fornulas and Completely Unitary Invariants for Some k-Tuples of Commuting Operators 367

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