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

Raul E. Curto

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

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

Journal article

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

Raul E. Curto

Transactions of the American Mathematical Society, Vol.266(1), pp.129-159

1981

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

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Abstract

Using J. L. Taylor’s definition of joint spectrum, we study Fredholm and invertible /i-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.

Deformation problem

Fredholm rt-tuple

Index

Joint essential spectrum

Toeplitz operator

Details

Title: Subtitle: Fredholm and invertible n-tuples of operators. The deformation problem
Creators: Raul E. Curto - University of Iowa, Mathematics
Resource Type: Journal article
Publication Details: Transactions of the American Mathematical Society, Vol.266(1), pp.129-159
DOI: 10.1090/S0002-9947-1981-0613789-6
ISSN: 0002-9947
Language: English
Date published: 1981
Academic Unit: Mathematics
Record Identifier: 9983985802302771

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