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Research on normal structure in a Banach space via some parameters in its dual space

Ji Gao
대한수학회 (The Korean Mathematical Society)|2019.04|대한수학회논문집 (Communications of the KMS)|제34권 제2호|pp. 465-475|DOI 10.4134/CKMS.c180108

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참고문헌

키워드

uniform normal structurenormal structureuniformly non-square space
주제분류수학

초록

Let $X$ be a Banach space and $X^*$ be its dual. In this paper, we give relationships among some parameters in $X^*$: $\varepsilon$-nonsquareness parameter, $J(\varepsilon,X^*)$; $\varepsilon$-boundary parameter, $Q(\varepsilon, X^*)$; the modulus of smoothness, $\rho_{X^*}(\varepsilon)$; and $\varepsilon$-Pythagorean parameter, $E(\varepsilon, X^*)$, and weak orthogonality parameter, $\omega(X)$ in $X$ that imply uniform norm structure in $X$. Some existing results are extended or approved.

Abstract

Let $X$ be a Banach space and $X^*$ be its dual. In this paper, we give relationships among some parameters in $X^*$: $\varepsilon$-nonsquareness parameter, $J(\varepsilon,X^*)$; $\varepsilon$-boundary parameter, $Q(\varepsilon, X^*)$; the modulus of smoothness, $\rho_{X^*}(\varepsilon)$; and $\varepsilon$-Pythagorean parameter, $E(\varepsilon, X^*)$, and weak orthogonality parameter, $\omega(X)$ in $X$ that imply uniform norm structure in $X$. Some existing results are extended or approved.

참고문헌 (25)

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