Banach space properties sufficient for normal structure

Abstract

In this paper we establish lower bounds for the weakly convergent sequence coefficient WCS(X) of a Banach space X, in terms of some well known moduli and coefficients. By mean of these bounds we identify several properties, of geometrical nature, which imply normal structure. We show that these properties are strictly more general than other previously known sufficient conditions for normal structure.

Wheeling around von Neumann–Jordan constant in Banach spaces

“…The characteristic of convexity of a Banach space X is defined as ε 0 (X) = sup{ε : δ X (ε) = 0}. E. M. Mazcuñán-Navarro [15] proved that for any Banach space X, C NJ (X) ≥ 1 + ε 0 (X) 2 /4. From (14) it follows immediately that also…”

Some geometric conditions which imply the fixed point property for multivalued nonexpansive mappings

“…• We can also show a condition (more general than ρ X (0) < 1/2) which gives an idea on how more general than the condition ρ X (0) < 1/2 hypothesis in Corollary 1 is. In [15] it is also proved that…”

“…Recently, E.M. Mazcuñán-Navarro [15] has established new lower bounds for the weakly convergent sequence coefficient WCS(X) of a Banach space X, in terms of the modulus of smoothness, the coefficient of weak orthogonality, the coefficient R(a, X), the James constant and the Jordan-von Neumann constant. By mean of these bounds, she identifies new geometrical properties which imply weak normal structure.…”

The Dunkl–Williams constant, convexity, smoothness and normal structure

“…This result has been recently generalized in [12]. We need to recall some definitions before stating this generalization.…”

“…The coefficient μ(X) ∈ [1, 3] was defined in [8] Theorem 13. (See Corollaries 11 and 28 in [12].) If X is a Banach space such that…”