Associate spaces

Ben Zion A. Rubshtein, Genady Ya Grabarnik, Mustafa A. Muratov, Yulia S. Pashkova

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

Abstract

In this chapter, we study associate spaces X1 of symmetric spaces X. The space X1 is defined by the duality 〈f, g〉= ∫fg dm, f ϵ X, g ϵ X1, and the norm ∥·∥X1 is induced by the canonical embedding of X1 into the dual space X* of X. We show that (X1, ∥·∥X1) is a symmetric space and that the canonical embedding of X1 into X* is surjective if and only if the space X is separable, i.e., X has property (A).

Original languageEnglish
Title of host publicationDevelopments in Mathematics
PublisherSpringer New York LLC
Pages83-93
Number of pages11
DOIs
StatePublished - 1 Jan 2016

Publication series

NameDevelopments in Mathematics
Volume45
ISSN (Print)1389-2177

ASJC Scopus subject areas

  • Mathematics (all)

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