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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

BCL index and Fredholm tuples


Author: Rongwei Yang
Journal: Proc. Amer. Math. Soc. 127 (1999), 2385-2393
MSC (1991): Primary 47C10; Secondary 47B35
Published electronically: April 9, 1999
MathSciNet review: 1605949
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Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • [BCL] 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 (57 #7251)
  • [Cu] R. Curto, Fredholm and invertible tuples of bounded linear operators, thesis, Math. Dept. of SUNY-Stonybrook 1978.
  • [Do] R. G. Douglas, Local Toeplitz operators, Proc. London Math. Soc. (3) 36 (1978), no. 2, 243–272. MR 0482348 (58 #2421)
  • [Ya] 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

DOI: http://dx.doi.org/10.1090/S0002-9939-99-04895-9
PII: S 0002-9939(99)04895-9
Received by editor(s): November 3, 1997
Published electronically: April 9, 1999
Communicated by: Theodore W. Gamelin
Article copyright: © Copyright 1999 American Mathematical Society