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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Logmodularity and isometries of operator algebras
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by David P. Blecher and Louis E. Labuschagne PDF
Trans. Amer. Math. Soc. 355 (2003), 1621-1646 Request permission

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
  • Email: dblecher@math.uh.edu
  • Louis E. Labuschagne
  • Affiliation: Department of Mathematics, Applied Mathematics and Astronomy, P.O. Box 392, 0003 UNISA, South Africa
  • MR Author ID: 254377
  • Email: labusle@unisa.ac.za
  • 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.
  • © Copyright 2002 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 355 (2003), 1621-1646
  • MSC (2000): Primary 46L07, 46J10, 46L52, 47L30; Secondary 46E25, 47B33
  • DOI: https://doi.org/10.1090/S0002-9947-02-03195-1
  • MathSciNet review: 1946408