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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



The generalized Fredholm operators

Author: Kung Wei Yang
Journal: Trans. Amer. Math. Soc. 216 (1976), 313-326
MSC: Primary 47B30; Secondary 47A55
MathSciNet review: 0423114
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Abstract: Let X, Y be Banach spaces over either the real field or the complex field. A continuous linear operator will be called a generalized Fredholm operator if $ T(X)$ is closed in Y, and Ker T and Coker T are reflexive Banach spaces. A theory similar to the classical Fredholm theory exists for the generalized Fredholm operators; and the similarity brings out the correspondence:

Reflexive Banach spaces $ \leftrightarrow $ finite-dimensional spaces,

weakly compact operators $ \leftrightarrow $ compact operators,

generalized Fredholm operators $ \leftrightarrow $ Fredholm operators,

Tauberian operators with closed range $ \leftrightarrow $ semi-Fredholm operators.

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Keywords: Generalized Fredholm operator, reflexive Banach space, weakly compact operator, Tauberian operator, exact sequence
Article copyright: © Copyright 1976 American Mathematical Society