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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

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


Author: Raul E. Curto
Journal: Trans. Amer. Math. Soc. 266 (1981), 129-159
MSC: Primary 47A53
MathSciNet review: 613789
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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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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1981-0613789-6
PII: S 0002-9947(1981)0613789-6
Keywords: Fredholm $ n$-tuple, index, deformation problem, joint essential spectrum, Toeplitz operator
Article copyright: © Copyright 1981 American Mathematical Society