Multivariable Operator Theory: A Joint Summer Research Conference on Multivariable Operator Theory, July 10-18, 1993, University of Washington, Seattle

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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.
 

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Contents

Explicit formulae for Taylors 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 and A 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
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 A2ℵ0 H
273
Higher order Hankel forms
283
Real valued spectral flow
307
Abstract resolutions for several commuting operators
319
Toeplitz C algebras and several complex variables
339
Positivity conditions and standard models for commuting multioperators
347

Algebraic Ktheory invariants for operator theory
187
Fundamentals of harmonic analysis on domains in complex space
195
Spectral picture and index invariants of commuting ntuples of operators
219
Trace formulas and completely unitary invariants for some ktuples of commuting operators
367
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