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Memoirs of the American Mathematical Society
1995; 53 pp; softcover
List Price: US$32
Individual Members: US$19.20
Institutional Members: US$25.60
Order Code: MEMO/117/559
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.
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