The Hille-Yosida space of an arbitrary operator

Shmuel Kantorovitz

Research output: Contribution to journalArticlepeer-review

28 Scopus citations

Abstract

Let A be an arbitrary Banach space operator with resolvent defined for all λ > 0. We define a linear manifold Z in the given space and a norm {triple vertical-rule fence}·{triple vertical-rule fence} on Z majorizing the given norm, such that (Z, {triple vertical-rule fence}·{triple vertical-rule fence}) is a Banach space, and the restriction of A to Z generates a strongly continuous semigroup of contractions in Z. This so-called Hille-Yosida space (Z, {triple vertical-rule fence}·{triple vertical-rule fence}) is "maximal-unique" in a suitable sense.

Original languageEnglish
Pages (from-to)107-111
Number of pages5
JournalJournal of Mathematical Analysis and Applications
Volume136
Issue number1
DOIs
StatePublished - 15 Nov 1988

Fingerprint

Dive into the research topics of 'The Hille-Yosida space of an arbitrary operator'. Together they form a unique fingerprint.

Cite this