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Logmodularity and isometries of operator algebras

Authors: David P. Blecher and Louis E. Labuschagne
Journal: Trans. Amer. Math. Soc. 355 (2003), 1621-1646
MSC (2000): Primary 46L07, 46J10, 46L52, 47L30; Secondary 46E25, 47B33
Published electronically: December 4, 2002
MathSciNet review: 1946408
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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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Additional Information

David P. Blecher
Affiliation: Department of Mathematics, University of Houston, Houston, Texas 77204-3008

Louis E. Labuschagne
Affiliation: Department of Mathematics, Applied Mathematics and Astronomy, P.O. Box 392, 0003 UNISA, South Africa

Received by editor(s): May 15, 2002
Received by editor(s) in revised form: September 4, 2002
Published electronically: December 4, 2002
Additional Notes: This research was supported in part by grants from the National Science Foundation and the University of South Africa.
Article copyright: © Copyright 2002 American Mathematical Society