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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.

References [Enhancements On Off] (What's this?)

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  • [2] M. Schechter, Basic theory of Fredholm operators, Ann. Scuola Norm. Sup. Pisa (3) 21 (1967), 261-280. MR 36 #6977. MR 0223930 (36:6977)
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Keywords: Five lemma, Banach space, category, ideal, abelian group, Fredholm operator, exact sequence
Article copyright: © Copyright 1977 American Mathematical Society

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