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Uniform G-Convexity for Vector-Valued Lp Spaces

Boyko, Nataliia; Kadets, Vladimir — 2009

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 46B20. Uniform G-convexity of Banach spaces is a recently introduced natural generalization of uniform convexity and of complex uniform convexity. We study conditions under which uniform G-convexity of X passes to the space of X-valued functions Lp (m,X).

On equivalent strictly G-convex renormings of Banach spaces

Nataliia Boyko — 2010

Open Mathematics

We study strictly G-convex renormings and extensions of strictly G-convex norms on Banach spaces. We prove that ℓω(Γ) space cannot be strictly G-convex renormed given Γ is uncountable and G is bounded and separable.

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