Dissipative operators and series inequalities


Of concern is the best constant K in the inequality Ax2 ≤ KA2xx 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. © 1981, Australian Mathematical Society. All rights reserved.

Publication Title

Bulletin of the Australian Mathematical Society