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Hilbert Modules over Operator Algebras
Paul S. Muhly and Baruch Solel
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Memoirs of the American Mathematical Society
1995; 53 pp; softcover
Volume: 117
ISBN-10: 0-8218-0346-8
ISBN-13: 978-0-8218-0346-2
List Price: US$32
Individual Members: US$19.20
Institutional Members: US$25.60
Order Code: MEMO/117/559
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This book gives a general systematic analysis of the notions of "projectivity" and "injectivity" in the context of Hilbert modules over operator algebras. A Hilbert module over an operator algebra \(A\) is simply the Hilbert space of a (contractive) representation of \(A\) viewed as a module over \(A\) in the usual way.

In this work, Muhly and Solel introduce various notions of projective Hilbert modules and use them to investigate dilation and commutant lifting problems over certain infinite dimensional analogues of incidence algebras.

The authors prove that commutant lifting holds for such an algebra if and only if the pattern indexing the algebra is a "tree" in the sense of computer directories.

Readership

Researchers in operator algebra.

Table of Contents

  • Introduction
  • Definitions
  • Basic theory
  • Incidence algebras and generalizations
  • Trees and trees
  • References
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