Logmodularity and isometries of operator algebras

Blecher, David; Labuschagne, Louis

doi:10.1090/S0002-9947-02-03195-1

Logmodularity and isometries of operator algebras
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by David P. Blecher and Louis E. Labuschagne

Trans. Amer. Math. Soc. 355 (2003), 1621-1646

DOI: https://doi.org/10.1090/S0002-9947-02-03195-1

Published electronically: December 4, 2002

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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 provided.

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