eBook ISBN:  9781470401382 
Product Code:  MEMO/117/559.E 
List Price:  $34.00 
MAA Member Price:  $30.60 
AMS Member Price:  $20.40 
eBook ISBN:  9781470401382 
Product Code:  MEMO/117/559.E 
List Price:  $34.00 
MAA Member Price:  $30.60 
AMS Member Price:  $20.40 

Book DetailsMemoirs of the American Mathematical SocietyVolume: 117; 1995; 53 ppMSC: Primary 47; 46;
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.
ReadershipResearchers in operator algebra.

Table of Contents

Chapters

1. Introduction

2. Definitions

3. Basic theory

4. Incidence algebras and generalizations

Appendix

5. Trees and trees


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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.
Researchers in operator algebra.

Chapters

1. Introduction

2. Definitions

3. Basic theory

4. Incidence algebras and generalizations

Appendix

5. Trees and trees