Paul S. Muhly's Books

Categories of Operator Modules (Morita Equivalence and Projective Modules)

Morita Equivalence and Projective Modules

By: David P. Blecher,Paul S. Muhly,Vern I. Paulsen

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Categories of Operator Modules (Morita Equivalence and Projective Modules)

Morita Equivalence and Projective Modules

By: David P. Blecher,Paul S. Muhly,Vern I. Paulsen

We employ recent advances in the theory of operator spaces, also known as quantized functional analysis, to provide a context in which one can compare categories of modules over operator algebras that are not necessarily self-adjoint. We focus our attention on the category of Hilbert modules over an operator algebra and on the category of operator modules over an operator algebra. The module operations are assumed to be completely bounded - usually, completely contractive. Wedevelop the notion of a Morita context between two operator algebras A and B. This is a system (A,B,{} {A}X {B},{} {B} Y {A},(\cdot,\cdot),[\cdot,\cdot]) consisting of the algebras, two bimodules {A}X {B and {B}Y {A} and pairings (\cdot,\cdot) and [\cdot,\cdot] that induce (complete) isomorphisms betweenthe (balanced) Haagerup tensor products, X \otimes {hB} {} Y and Y \otimes {hA} {} X, and the algebras, A and B, respectively. Thus, formally, a Morita context is the same as that which appears in pure ring theory. The subtleties of the theory lie in the interplay between the pure algebra and the operator space geometry. Our analysis leads to viable notions of projective operator modules and dual operator modules. We show that two C*-algebras are Morita equivalent in our sense if and only ifthey are C*-algebraically strong Morita equivalent, and moreover the equivalence bimodules are the same. The distinctive features of the non-self-adjoint theory are illuminated through a number of examples drawn from complex analysis and the theory of incidence algebras over topological partial orders.Finally, an appendix provides links to the literature that developed since this Memoir was accepted for publication.

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Page Count

109

Publisher

American Mathematical Soc.

Published Date

ISBN 10

082181916X

ISBN 13

9780821819166

Hilbert Modules over Operator Algebras

By: Paul S. Muhly,Baruch Solel

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Hilbert Modules over Operator Algebras

By: Paul S. Muhly,Baruch Solel

Addresses the three-dimensional generalization of category, offering a full definition of tricategory; a proof of the coherence theorem for tricategories; and a modern source of material on Gray's tensor product of 2-categories. Of interest to research mathematicians; theoretical physicists, algebraic topologists; 3-D computer scientists; and theoretical computer scientists. Society members, $19.00. No index. Annotation copyright by Book News, Inc., Portland, OR

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American Mathematical Soc.

Published Date

ISBN 10

0821803468

ISBN 13

9780821803462

Excluding Infinite Clique Minors

By: Neil Robertson,Paul D. Seymour,Robin Thomas

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Excluding Infinite Clique Minors

By: Neil Robertson,Paul D. Seymour,Robin Thomas

For each infinite cardinal [lowercase Greek]Kappa, we give a structural characterization of the graphs with no [italic capital]K[subscript lowercase Greek]Kappa minor. We also give such a characterization of the graphs with no "half-grid" minor.

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Page Count

116

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821804022

ISBN 13

9780821804025

Analytic Deformations of the Spectrum of a Family of Dirac Operators on an Odd-Dimensional Manifold with Boundary

By: Paul Kirk,Eric Klassen

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Analytic Deformations of the Spectrum of a Family of Dirac Operators on an Odd-Dimensional Manifold with Boundary

By: Paul Kirk,Eric Klassen

The analytic perturbation theory for eigenvalues of Dirac operators on odd dimensional manifolds with boundary is described in terms of [italic]extended L2 eigenvectors [end italics] on manifolds with cylindrical ends. These are generalizations of the Atiyah-Patodi-Singer extended [italic capital]L2 kernel of a Dirac operator. We prove that they form a discrete set near zero and deform analytically, in contrast to [italic capital]L2 eigenvectors, which can be absorbed into the continuous spectrum under deformations when the tangential operator is not invertible. We show that the analytic deformation theory for extended [italic capital]L2 eigenvectors and Atiyah-Patodi-Singer eigenvectors coincides.

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American Mathematical Soc.

Published Date

ISBN 10

082180538X

ISBN 13

9780821805381

Poisson Structures and Their Normal Forms

By: Jean-Paul Dufour,Nguyen Tien Zung

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Poisson Structures and Their Normal Forms

By: Jean-Paul Dufour,Nguyen Tien Zung

The aim of this book is twofold. On the one hand, it gives a quick, self-contained introduction to Poisson geometry and related subjects. On the other hand, it presents a comprehensive treatment of the normal form problem in Poisson geometry. Even when it comes to classical results, the book gives new insights. It contains results obtained over the past 10 years which are not available in other books.

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Page Count

332

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3764373350

ISBN 13

9783764373351

Homotopy Theory: Relations with Algebraic Geometry, Group Cohomology, and Algebraic $K$-Theory

Relations with Algebraic Geometry, Group Cohomology, and Algebraic K-theory : an International Conference on Algebraic Topology, March 24-28, 2002, Northwestern University

By: Paul Gregory Goerss,Stewart Priddy

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Homotopy Theory: Relations with Algebraic Geometry, Group Cohomology, and Algebraic $K$-Theory

Relations with Algebraic Geometry, Group Cohomology, and Algebraic K-theory : an International Conference on Algebraic Topology, March 24-28, 2002, Northwestern University

By: Paul Gregory Goerss,Stewart Priddy

As part of its series of Emphasis Years in Mathematics, Northwestern University hosted an International Conference on Algebraic Topology. The purpose of the conference was to develop new connections between homotopy theory and other areas of mathematics. This proceedings volume grew out of that event. Topics discussed include algebraic geometry, cohomology of groups, algebraic $K$-theory, and $\mathbb{A 1$ homotopy theory. Among the contributors to the volume were Alejandro Adem,Ralph L. Cohen, Jean-Louis Loday, and many others. The book is suitable for graduate students and research mathematicians interested in homotopy theory and its relationship to other areas of mathematics.

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Page Count

520

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821832859

ISBN 13

9780821832851

Cyclic Phenomena for Composition Operators

By: Paul Bourdon,Joel H. Shapiro

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Cyclic Phenomena for Composition Operators

By: Paul Bourdon,Joel H. Shapiro

We undertake a systematic study of cyclic phenomena for composition operators. Our work shows that composition operators exhibit strikingly diverse types of cyclic behavior, and it connects this behavior with classical problems involving complex polynomial approximation and analytic functional equations.

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Page Count

122

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821806300

ISBN 13

9780821806302

On Natural Coalgebra Decompositions of Tensor Algebras and Loop Suspensions

By: Paul Selick,Jie Wu

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On Natural Coalgebra Decompositions of Tensor Algebras and Loop Suspensions

By: Paul Selick,Jie Wu

This book is intended for graduate students and research mathematicians interested in topology and representation theory.

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Page Count

122

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821821105

ISBN 13

9780821821107

Book's by Paul S. Muhly

Categories of Operator Modules (Morita Equivalence and Projective Modules)

Categories of Operator Modules (Morita Equivalence and Projective Modules)

Hilbert Modules over Operator Algebras

Hilbert Modules over Operator Algebras

Excluding Infinite Clique Minors

Excluding Infinite Clique Minors

Analytic Deformations of the Spectrum of a Family of Dirac Operators on an Odd-Dimensional Manifold with Boundary

Analytic Deformations of the Spectrum of a Family of Dirac Operators on an Odd-Dimensional Manifold with Boundary

Poisson Structures and Their Normal Forms

Poisson Structures and Their Normal Forms

Homotopy Theory: Relations with Algebraic Geometry, Group Cohomology, and Algebraic $K$-Theory

Homotopy Theory: Relations with Algebraic Geometry, Group Cohomology, and Algebraic $K$-Theory

Cyclic Phenomena for Composition Operators

Cyclic Phenomena for Composition Operators

On Natural Coalgebra Decompositions of Tensor Algebras and Loop Suspensions

On Natural Coalgebra Decompositions of Tensor Algebras and Loop Suspensions

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