On the sum of proximinal subspaces
โ 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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๐ SIMILAR VOLUMES
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
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
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).