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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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BCL index and Fredholm tuples
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by Rongwei Yang PDF
Proc. Amer. Math. Soc. 127 (1999), 2385-2393 Request permission

Abstract:

In this paper we will prove that the BCL index for $C^*$-algebras generated by two essentially doubly commuting isometries is equal to the index of the Fredholm tuples formed by these two isometries. We will then compute this index for certain sub-Hardy modules over the bidisk. Some interesting corollaries are also listed.
References
  • C. A. Berger, L. A. Coburn, and A. Lebow, Representation and index theory for $C^*$-algebras generated by commuting isometries, J. Functional Analysis 27 (1978), no. 1, 51–99. MR 0467392, DOI 10.1016/0022-1236(78)90019-8
  • R. Curto, Fredholm and invertible tuples of bounded linear operators, thesis, Math. Dept. of SUNY-Stonybrook 1978.
  • R. G. Douglas, Local Toeplitz operators, Proc. London Math. Soc. (3) 36 (1978), no. 2, 243–272. MR 482348, DOI 10.1112/plms/s3-36.2.243
  • R. Yang, The Berger-Shaw theorem in Hardy modules over the bidisk, submitted to J. of Operator Theory.
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Additional Information
  • Rongwei Yang
  • Affiliation: Department of Mathematics, Texas A&M University, College Station, Texas 77843; Department of Mathematics, SUNY at Stony Brook, Stony Brook, New York 11794
  • Email: ryang@math.tamu.edu
  • Received by editor(s): November 3, 1997
  • Published electronically: April 9, 1999
  • Communicated by: Theodore W. Gamelin
  • © Copyright 1999 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 127 (1999), 2385-2393
  • MSC (1991): Primary 47C10; Secondary 47B35
  • DOI: https://doi.org/10.1090/S0002-9939-99-04895-9
  • MathSciNet review: 1605949