Hilbert Modules over Operator Algebras

Paul S. Muhly · Baruch Solel

1995年1月 · American Mathematical Society: Memoirs of the American Mathematical Society 第 559 本图书 · American Mathematical Soc.

关于此电子书

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.