Logmodularity and isometries of operator algebras

2002/05/14 by David P. Blecher, Blecher, David P., Louis E. Labuschagne +1
Mathematics · #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA) #math.FA #math.OA

paper · pdf · doi:10.48550/arxiv.math/0205159

24 pages

arxiv created 2002/05/14 · arxiv updated 2009/11/30

Abstract

We generalize some facts about function algebras to operator algebras, using the `noncommutative Shilov boundary' or C^*-envelope first considered by Arveson. In the first part we study and characterize complete isometries between operator algebras. In the second part we introduce and study a notion of logmodularity for operator algebras. We also give a result on conditional expectations. Many miscellaneous applications are given.

Related

• Complete isometries - an illustration of noncommutative functional analysis
• The Shilov boundary of an operator space - and the characterization theorems
• Representations of logmodular algebras
• Multipliers and dual operator algebras
• Real Operator Algebras and Real Completely Isometric Theory