Fredholm and invertible 𝑛-tuples of operators. The deformation problem

Curto, Raul E.

doi:10.1090/S0002-9947-1981-0613789-6

Fredholm and invertible $n$-tuples of operators. The deformation problem
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by Raul E. Curto PDF

Trans. Amer. Math. Soc. 266 (1981), 129-159 Request permission

Abstract:

Using J. L. Taylor’s definition of joint spectrum, we study Fredholm and invertible $n$-tuples of operators on a Hilbert space. We give the foundations for a "several variables" theory, including a natural generalization of Atkinson’s theorem and an index which well behaves. We obtain a characterization of joint invertibility in terms of a single operator and study the main examples at length. We then consider the deformation problem and solve it for the class of almost doubly commuting Fredholm pairs with a semi-Fredholm coordinate.

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