Nearly Strict Convexity and Best Approximation

近严格凸与最佳逼近(英文)

In this paper, we study nearly strict convexity and the best approximation in nearly strictly convex spaces. We prove that a Banach space X is nearly strictly convex if and only if all of the subspaces of X are compact semi Chebyshev subspaces. We also show that Theorem 6 in is false.

本文研究近严格凸与最佳逼近的关系．证明了Ｂａｎａｃｈ空间Ｘ是近严格凸的当且仅当Ｘ的每个子空间是紧－半－切比晓夫空间．