On Ψ direct sums of Banach spaces and convexity

Journal of the Australian Mathematical Society

Mikio Kato¹ 

[1] Kichi-Suke Saito

关键词: primary 46B20;    46B99;    26A51;    52A21;    90C25;   

DOI  :  10.1017/S1446788700008193

学科分类：数学（综合）

来源: Cambridge University Press

【 摘 要 】

Let 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.

【 授权许可】

Unknown