TY - CHAP

T1 - Associate spaces

AU - Rubshtein, Ben Zion A.

AU - Grabarnik, Genady Ya

AU - Muratov, Mustafa A.

AU - Pashkova, Yulia S.

N1 - Publisher Copyright:
© Springer International Publishing Switzerland 2016.

PY - 2016/1/1

Y1 - 2016/1/1

N2 - 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).

AB - 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).

UR - http://www.scopus.com/inward/record.url?scp=85006298260&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-42758-4_7

DO - 10.1007/978-3-319-42758-4_7

M3 - Chapter

AN - SCOPUS:85006298260

T3 - Developments in Mathematics

SP - 83

EP - 93

BT - Developments in Mathematics

PB - Springer New York LLC

ER -