On the modulus of U‐convexity
Copyright policy )On the modulus of U‐convexity
We prove that the moduli of U‐convexity, introduced by Gao (1995), of the ultrapower of a Banach space X and of X itself coincide whenever X is super‐reflexive. As a consequence, some known results have been proved and improved. More precisely, we prove that uX(1) > 0 implies that both X and the dual space X∗ of X have uniform normal structure and hence the “worth” property in Corollary 7 of Mazcuñán‐Navarro (2003) can be discarded.
- Khon Kaen University Thailand
Banach spaces, uniform normal structure, Geometry and structure of normed linear spaces, Fixed-point theorems, Uniform normal structure, modulus of \(U\)-convexity, QA1-939, Modulus of W∗-convexity, Super-reflexive space, superreflexivity, Mathematics
Banach spaces, uniform normal structure, Geometry and structure of normed linear spaces, Fixed-point theorems, Uniform normal structure, modulus of \(U\)-convexity, QA1-939, Modulus of W∗-convexity, Super-reflexive space, superreflexivity, Mathematics
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