On Ψ direct sums of Banach spaces and convexity
2003 ◽
Vol 75
(3)
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pp. 413-422
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Keyword(s):
AbstractLet X1, X2, …, XN be Banach spaces and ψ a continuous convex function with some appropriate conditions on a certain convex set in RN−1. Let (X1⊕X2⊕…⊕XN)Ψ be the direct sum of X1, X2, …, XN equipped with the norm associated with Ψ. We characterize the strict, uniform, and locally uniform convexity of (X1 ⊕ X2 ⊕ … ⊕ XN)Ψ; by means of the convex function Ψ. As an application these convexities are characterized for the ℓp, q-sum (X1 ⊕ X2 ⊕ … ⊕ XN)p, q (1 < q ≤ p ≤ ∈, q < ∞), which includes the well-known facts for the ℓp-sum (X1 ⊕ X2 ⊕ … ⊕ XN)p in the case p = q.
2003 ◽
Vol 277
(1)
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pp. 1-11
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Keyword(s):
2017 ◽
Vol 60
(4)
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pp. 791-806
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Keyword(s):
2010 ◽
Vol 8
(2)
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pp. 346-356
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1994 ◽
Vol 17
(4)
◽
pp. 661-666
Keyword(s):
1981 ◽
Vol 33
(4)
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pp. 817-825
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Keyword(s):