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

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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 |

### Other editions - View all

Multivariable Operator Theory: A Joint Summer Research Conference on ... Raúl E. Curto No preview available - 1995 |

### Common terms and phrases

adjoint Alg(C Amer analytic functions Banach space Bergman kernel Bergman space boundary bounded operators bounded symmetric domains C*-algebra Cartan domain commuting n-tuple compact complete unitary invariant completely distributive condition Conjecture contractive Corollary corresponding decomposition defined definition denote differential dilation element example exists finite formula Fréchet Fredholm function f functional calculus geometry H & H Hankel forms Hankel operators Hardy space Hence Hilbert modules Hilbert space holomorphic functions homogeneous type homotopy implies inner product integral invariant subspaces isomorphism K-theory Koszul complex Lemma linear Math matrix n-tuple nest algebra Neumann algebra norm obtain Operator Theory orthogonal polydisk polynomials positive preprint problem projection proof Proposition prove pseudoconvex domains representation representing measure reproducing kernel resolution result Section sequence sheaf sheaves spectral spectrum strongly pseudoconvex subnormal subset tensor product Theorem Toeplitz operators topological tuples unique unit ball unitarily equivalent variables vector