Modules over operator algebras, and the maximal C^*-dilation
Operator Algebras
2007-05-23 v1
Abstract
We continue our study of the general theory of possibly nonselfadjoint algebras of operators on a Hilbert space, and modules over such algebras, developing a little more technology to connect `nonselfadjoint operator algebra' with the Calgebraic framework. More particularly, we make use of the universal, or maximal, Calgebra generated by an operator algebra, and Cdilations. This technology is quite general, however it was developed to solve some problems arising in the theory of Morita equivalence of operator algebras, and as a result most of the applications given here (and in a companion paper) are to that subject. Other applications given here are to extension problems for module maps, and characterizations of Calgebras.
Keywords
Cite
@article{arxiv.math/9906081,
title = {Modules over operator algebras, and the maximal C^*-dilation},
author = {David P. Blecher},
journal= {arXiv preprint arXiv:math/9906081},
year = {2007}
}