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Raul E. Curio, Ronald G. Douglas, Joel D. Pincus, Norberto Salinas, "Multivariable Operator Theory"

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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