Weak Lp-stability of a linear semigroup on a Hilbert space implies exponential stability

George Weiss*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

We prove that a strongly continuous semigroup of linear operators on a Hilbert space is weakly Lp-stable for some p ε{lunate} [1, ∞) if and only if the semigroup is exponentially stable. As an application, we prove that the Cauchy problems associated with the semigroup are well posed on the infinite time interval (- ∞, 0] if and only if the semigroup is exponentially stable.

Original languageEnglish
Pages (from-to)269-285
Number of pages17
JournalJournal of Differential Equations
Volume76
Issue number2
DOIs
StatePublished - Dec 1988
Externally publishedYes

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