Stability of ball proximinality
نویسندگان
چکیده
منابع مشابه
Stability of ball proximinality
In this paper, we show that if E is an order continuous Köthe function space and Y is a separable subspace ofX, 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-uncondi...
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A known, and easy to establish, fact in Best Approximation Theory is that, if the unit ball of a subspace G of a Banach space X is proximinal in X, then G itself is proximinal in X. We are concerned in this article with the reverse implication, as the knowledge of whether the unit ball is proximinal or not is useful in obtaining information about other problems. We show, by constructing a count...
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ژورنال
عنوان ژورنال: Journal of Approximation Theory
سال: 2014
ISSN: 0021-9045
DOI: 10.1016/j.jat.2014.04.008