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Embedding weakly compact sets into Hilbert space

โœ Scribed by Y. Benyamini; T. Starbird

Book ID
112884246
Publisher
The Hebrew University Magnes Press
Year
1976
Tongue
English
Weight
218 KB
Volume
23
Category
Article
ISSN
0021-2172

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We use properties of Day's norm on c 0 (}) to prove that, for every Eberlein compact space K, there exists a separately continuous symmetric mapping d: K\_K ร„ R such that we have d(x, y)< d(x, x)+d( y, y) 2 for any two distinct points x and y of K. As a consequence, we have that every Eberlein compa

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The C 1 -Weierstrass approximation theorem is proved for any compact subset X of a Hilbert space H. The same theorem is also proved for Whitney 1-jets on X when X satisfies the following further condition: There exist finite dimensional linear subspaces n 1 H n is dense in span{X} and ฯ€ n (X) = X โˆฉ