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Equisummability for linear operators in Banach spaces

Published online by Cambridge University Press:  14 November 2011

M. A. Kon ,
A. G. Ramm  and
L. A. Raphael
M. A. Kon
Affiliation:
Department of Mathematics, Columbia University, New York, NY 10027, U.S.A.
A. G. Ramm
Affiliation:
Department of Mathematics, Kansas State University, Manhattan, KS 66506, U.S.A.
L. A. Raphael
Affiliation:
Department of Mathematics, Howard University, Washington, DC 20059, U.S.A.
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Synopsis

Let A and B be closed linear operators on a Banach space X. Assume that ε(εI – A)−1f→f as |ε|→ ∞ for all f in X, ζ∊∑ ⊂ℂ. Under what conditions on B − A does the same relationship hold for B? When does [ε(εI − A)−1 − ε(εI − B)−1 ] f→ 0 in some stronger norm than that of X? The questions are discussed in an abstract setting and the results are generalised to other analytic functions of A. Applications are given to second order elliptic operators.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 106 , Issue 3-4 , 1987 , pp. 315 - 325
Copyright
Copyright © Royal Society of Edinburgh 1987

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