# Selfadjoint and Nonselfadjoint Operator Algebras and Operator Theory

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*Robert S. Doran*

This book contains papers presented at the NSF/CBMS Regional Conference on Coordinates in Operator Algebras, held at Texas Christian University in Fort Worth in May 1990. During the conference, in addition to a series of ten lectures by Paul S. Muhly (which will be published in a CBMS Regional Conference Series volume), twenty-eight lectures were delivered by conference participants on a broad range of topics of current interest in operator algebras and operator theory. This volume contains slightly expanded versions of most of those lectures. Participants were encouraged to bring open problems to the conference, and, as a result, over one hundred problems and questions are scattered throughout this volume. Readers will appreciate this book for the overview it provides of current topics and methods of operator algebras and operator theory.

# Table of Contents

## Selfadjoint and Nonselfadjoint Operator Algebras and Operator Theory

- Contents xi12 free
- Preface xv16 free
- Conference participants xvii18 free
- C*-algebras associated to two-step nilpotent groups 124 free
- Some applications of a recent characterization of operator algebras 730
- Problems in multivariable operator theory 1538
- The Taylor spectrum of infinite direct sums 1942
- Operator algebras and differential topology 2952
- Operator algebras with arbitrary Hochschild cohomology 3356
- Representation of symplectic vector spaces obtained as unitary dilations 4164
- Imprimitivity systems associated to regions in Rn, connections between geometry and spectrum, a sample of problems 6184
- Triangular algebras — another chapter 6386
- Decomposability of operators relative to two subspaces 77100
- The equation Tx = y in nest algebras 83106
- Some questions concerning nest algebras 89112
- Some problems on triangular and semi-triangular operators 97120
- Two problems on almost diagonalization of normal operators 101124
- Spatial implementation of lattice isomorphisms 113136
- Intrinsic isomorphism invariants for some triangular operator algebras 117140
- Some operator-algebraic aspects of the theory of infinite graphs 123146
- On analytic subalgebras of UHF algebras 127150
- Five problems on operator algebras 133156
- Analytic triangular algebras with integer valued cocycle 139162
- Fourier-Stieltjes algebras of locally compact groupoids 143166
- On the preduals of dual algebras and their tensor products 157180
- An introduction to Toeplitz operators associated with analytic crossed products 165188
- Distance formula and contractive projections 169192
- Constructions of extreme n-positive linear maps 175198
- Duality for actions and coactions of measured groupoids on von Neumann algebras 183206
- Cyclic cohomology and the index theory of transversely elliptic operators 189212
- Ideals of generalized Calkin algebras 193216
- Problems on C*-algebras of real rank zero and their multiplier algebras 199222
- A collection of problems on operator algebras 205228
- The Texas Groupoid in King Robert's Court 215238