A Note on Semi-Fredholm Hilbert Modules
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.
KeywordsHilbert modules quasi-free Hilbert modules Fredholm tuple Corona property
Mathematics Subject Classification (2000)47A13 46E22 46M20 47B32
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