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On the sum of proximinal subspaces

โœ Scribed by Moshe Feder


Publisher
Elsevier Science
Year
1987
Tongue
English
Weight
150 KB
Volume
49
Category
Article
ISSN
0021-9045

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๐Ÿ“œ SIMILAR VOLUMES


Proximinality in Subspaces of c0
โœ G. Godefroy; V. Indumathi ๐Ÿ“‚ Article ๐Ÿ“… 1999 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 94 KB

We say that a normed linear space X is a R(1) space if the following holds: If Y is a closed subspace of finite codimension in X and every hyperplane containing Y is proximinal in X then Y is proximinal in X. In this paper we show that any closed subspace of c 0 is a R(1) space. ## 1999 Academic Pr

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Let < be a "nite additive subgroup of a "eld K of characteristic p'0. We consider sums of the form S F (< : )" TZ4 (v# )F for h50 and 3 K. In particular, we give necessary and su$cient conditions for the vanishing of S F (<; ), in terms of the digit sum in the base-p expansion of h, in the case that

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It is shown that if A is a unital C\*-algebra then Z(A), the centre of A, is a proximinal subspace. In other words, for each a # A there exists z # Z(A) such that &a&z& is equal to the distance from a to Z(A).