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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

The five lemma for Banach spaces


Author: A. J. Pryde
Journal: Proc. Amer. Math. Soc. 65 (1977), 37-43
MSC: Primary 46M20; Secondary 47A50
MathSciNet review: 0450998
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Abstract: We prove a version of the five lemma which is useful for the study of boundary value problems for partial differential equations. The results are given in the category $ \mathcal{B}$ of Banach spaces and bounded linear operators, and all conditions are stated modulo an arbitrary ideal of $ \mathcal{B}$. We also show that the results are valid in more general categories.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1977-0450998-8
PII: S 0002-9939(1977)0450998-8
Keywords: Five lemma, Banach space, category, ideal, abelian group, Fredholm operator, exact sequence
Article copyright: © Copyright 1977 American Mathematical Society