**Memoirs of the American Mathematical Society**

1995;
53 pp;
Softcover

MSC: Primary 47; 46;

Print ISBN: 978-0-8218-0346-2

Product Code: MEMO/117/559

List Price: $34.00

AMS Member Price: $20.40

MAA Member Price: $30.60

**Electronic ISBN: 978-1-4704-0138-2
Product Code: MEMO/117/559.E**

List Price: $34.00

AMS Member Price: $20.40

MAA Member Price: $30.60

# Hilbert Modules over Operator Algebras

Share this page
*Paul S. Muhly; Baruch Solel*

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.