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A Note on Semi-Fredholm Hilbert Modules

  • Ronald G. Douglas
  • Jaydeb Sarkar
Part of the Operator Theory: Advances and Applications book series (OT, volume 202)

Abstract

A classical problem in operator theory has been to determine the spectrum of Toeplitz-like operators on Hilbert spaces of vector-valued holomorphic functions on the open unit ball in ℂ m . In this note we obtain necessary conditions for k-tuples of such operators to be Fredholm in the sense of Taylor and show they are sufficient in the case of the unit disk.

Keywords

Hilbert modules quasi-free Hilbert modules Fredholm tuple Corona property 

Mathematics Subject Classification (2000)

47A13 46E22 46M20 47B32 

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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2010

Authors and Affiliations

  • Ronald G. Douglas
    • 1
  • Jaydeb Sarkar
    • 1
  1. 1.Texas A & M UniversityCollege StationTexasUSA

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