SMOOTH POINTS OF VECTOR VALUED FUNCTION SPACES

If E is a Banach space, then an element x ϵ E, ∥x∥ = 1 is called smooth if there is a unique x* ϵ E*, ∥x*∥ = 1 such that ❬x*,x❭ = 1. The object of this paper is characterize the smooth points of LP(I, X), lp(X), 1 ≤ p < ∞, where X is some Banach space. Some other related results are presented....

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Bibliographic Details
Published in:The Rocky Mountain journal of mathematics 1994, Vol.24 (2), p.505-512
Main Authors: DEEB, W., KHALIL, R.
Format: Article
Language:English
Subjects:
Banach space
Mathematical theorems
Tensors
Unit ball
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Summary:If E is a Banach space, then an element x ϵ E, ∥x∥ = 1 is called smooth if there is a unique x* ϵ E*, ∥x*∥ = 1 such that ❬x*,x❭ = 1. The object of this paper is characterize the smooth points of LP(I, X), lp(X), 1 ≤ p < ∞, where X is some Banach space. Some other related results are presented.
ISSN:0035-7596
1945-3795
DOI:10.1216/rmjm/1181072414