The generalized Fredholm operators
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- by Kung Wei Yang
- Trans. Amer. Math. Soc. 216 (1976), 313-326
- DOI: https://doi.org/10.1090/S0002-9947-1976-0423114-X
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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.References
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Bibliographic Information
- © Copyright 1976 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 216 (1976), 313-326
- MSC: Primary 47B30; Secondary 47A55
- DOI: https://doi.org/10.1090/S0002-9947-1976-0423114-X
- MathSciNet review: 0423114