REMOTALITY OF CERTAIN SETS Lp I,X

Year 2014, Volume: 4 Issue: 2, 209 - 215, 01.12.2014

Sharifa Al-sharif Alhassan Alshorman

Abstract

Let X be a Banach space and let I, Ω, µ be a measure space. For 1 ≤ p < ∞, let L p I, X denote the space of Bochner p−integrable functions defined on I with values in X. The object of this paper is to give sufficient conditions for remotality of L 1 I, H + L 1 I, G in L 1 I, X , where H and G are two bounded sets in X which include as a special case remotality of L 1 I ∧ ⊗ G + H ∧ ⊗ L 1 I in L 1 I × I .

Keywords

Remotal set, Bochner p−integrable function, Banach space

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