Logmodularity and isometries of operator algebras

Details Logmodularity and isometries of operator algebras Logmodularity and isometries of operator algebras

2002-05-14

arxiv.org/abs/math/0205159v1

Mathematics

Operator Algebras

24 pages

Scientific paper

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.

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