REMOTALITY OF CERTAIN SETS Lp(I,X)

REMOTALITY OF CERTAIN SETS Lp(I,X)

Sharifa Al-Sharifi, Alhassan Alshorman

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Abstract

Let X be a Banach space and let (I , Ω, µ) be a measure space. For 1 ≤ p < ∞, let Lp (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 sufficent conditions for remotality of L1 (I , H ) + L1 (I , G) in L1 (I , X ), where H and G are two bounded sets in X which include as a special case remotality of L1(I)^⊗G+H^⊗L1(I)inL1(I×I).

Keywords

Remotal set, Bochner p−integrable function, Banach space.