Hilbert Modules over Operator Algebras: 117 (Memoirs of the AMS) (Memoirs of the American Mathematical Society) - Softcover

American Mathematical Society

Softcover

ISBN 10: 0821803468 ISBN 13: 9780821803462

Publisher: American Mathematical Society, 1995

Synopsis

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.

Edition details

• Publisher: American Mathematical Society
• Publication date: 1995
• Language: English
• ISBN 10: 0821803468
• ISBN 13: 9780821803462
• Binding: Paperback