Author： Al-Sharif Sh.
Publisher： Taylor & Francis Ltd
ISSN： 0163-0563
Source： Numerical Functional Analysis and Optimization, Vol.32, Iss.3, 2011-03, pp. : 233-242
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Abstract
Let X be a Banach space, (I, μ) be a finite measure space. By LΦ(I, X), let us denote the space of all X-valued Bochner Orlicz integrable functions on the unit interval I equipped with the Luxemburg norm. A closed bounded subset G of X is called remotal if for any x ∈ X, there exists g ∈ G such that ‖x - g‖ = ρ(x, G) = sup {‖x - y‖: y ∈ G}. In this article, we show that for a separable remotal set G ⊂ X, the set of Bochner integrable functions, LΦ(I, G) is remotal in LΦ(I, X). Some other results are presented.
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