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Dissipative operators and series inequalities

Published online by Cambridge University Press:  17 April 2009

Herbert A. Gindler  and
Jerome A. Goldstein
Herbert A. Gindler
Affiliation:
Department of Mathematics, San Diego State University, San Diego, California 92182, USA
Jerome A. Goldstein
Affiliation:
Department of Mathematics, Tulane University, New Orleans, Louisiana 70118, USA.
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Abstract

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Of concern is the best constant K in the inequality ‖Ax‖2 ≤ K‖A2x‖‖x‖ where A generates a strongly continuous contraction semigroup in a Hilbert space. Criteria are obtained for approximate extremal vectors x when K = 2 (K ≤ 2 always holds). By specializing A + I to be a shift operator on a sequence space, very simple proofs of Copson's recent results on series inequalities follow. Inequalities of the above type are also studied on LP spaces, and earlier results of the authors and of Holbrook are improved.

Information

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 23 , Issue 3 , June 1981 , pp. 429 - 442
Copyright
Copyright © Australian Mathematical Society 1981

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