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).
|Title of host publication||Developments in Mathematics|
|Publisher||Springer New York LLC|
|Number of pages||11|
|State||Published - 1 Jan 2016|
|Name||Developments in Mathematics|
ASJC Scopus subject areas
- Mathematics (all)