English

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 C^*-algebraic framework. More particularly, we make use of the universal, or maximal, C^*-algebra generated by an operator algebra, and C^*-dilations. 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 C^*-algebras.

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}
}