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Logmodularity and isometries of operator algebras

David P. Blecher·Louis E. Labuschagne
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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.

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David P. Blecher, Louis E. Labuschagne. 2002-05-14. Logmodularity and isometries of operator algebras. https://arxiv.org/abs/math/0205159

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