Modules over operator algebras, and the maximal C^*-dilation

1999/06/12 by David P. Blecher, Blecher, David P. · 1 citation
Mathematics · #47D25 #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Holomorphic and Operator Theory #Operator Algebras (math.OA) #math.OA #msc:47D25

paper · pdf · doi:10.48550/arxiv.math/9906081

arxiv created 1999/06/12 · openalex publication_date 1999/06/12 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Morita equivalence for c∗-algebras and w∗-algebras
• Subalgebras of C*-algebras
• A Morita theorem for algebras of operators on Hilbert space

Cited by

• Couniversality for C*-algebras of residually finite-dimensional operator algebras

Related

• Extensions and Dilations of module maps
• The Shilov boundary of an operator space - and the characterization theorems
• Hilbert H*-modules and Hilbert modules over (non-self-adjoint) operator algebras -- a reference overview II
• Operator Models for Hilbert Locally C^*-Modules
• Hilbert C*-modules and related subjects - a guided reference overview I