Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4607102 | Journal of Approximation Theory | 2014 | 10 Pages |
Abstract
In this paper, we show that if E is an order continuous Köthe function space and Y is a separable subspace of X, then E(Y) is ball proximinal in E(X) if and only if Y is ball proximinal in X. As a consequence, E(Y) is proximinal in E(X) if and only if Y is proximinal in X. This solves an open problem of Bandyopadhyay, Lin and Rao. It is also shown that if E is a Banach lattice with a 1-unconditional basis and for each n, Yn is a subspace of Xn, then (âYn)E is ball proximinal in (âXn)E if and only if each Yn is ball proximinal in Xn.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Pei-Kee Lin, Wen Zhang, Bentuo Zheng,