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Published in:
2016 | OriginalPaper | Chapter
6. Embeddings. Minimality and Separability. Property (A)
Authors : Ben-Zion A. Rubshtein, Genady Ya. Grabarnik, Mustafa A. Muratov, Yulia S. Pashkova
Published in: Foundations of Symmetric Spaces of Measurable Functions
Publisher: Springer International Publishing
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Abstract
In this chapter we study minimal and separable symmetric spaces. The minimal part X
0 of a symmetric space X is the closure of L
1 ∩L
∞
in X, and X is minimal if X
0 = X. We show that every separable symmetric space is minimal, and the converse is true under the additional condition ϕ
X
(0+) = 0. We consider also an important property (A), which is equivalent to separability.