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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.
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참고문헌 신청
M. S. Brodskii / 1948 / On the center of a convex set / Doklady Akad. Nauk SSSR (N.S.) 59:837~840
D. Dacunha-Castelle / 1972 / Applications des ultraproduits a l'etude des espaces et des algebres de Banach / Studia Math 41:315~334
M. M. Day / 1973 / Normed Linear Spaces / Springer-Verlag
J. Diestel / 1975 / Geometry of Banach spaces|selected topics / Springer-Verlag
D. van Dulst / 1984 / Some more Banach spaces with normal structure / J. Math. Anal. Appl 104(1):285~292
D. Dacunha-Castelle / 1972 / Applications des ultraproduits a l'etude des espaces et des algebres de Banach / Studia Math 41:315~334
M. M. Day / 1973 / Normed Linear Spaces / Springer-Verlag
J. Diestel / 1975 / Geometry of Banach spaces|selected topics / Springer-Verlag
D. van Dulst / 1984 / Some more Banach spaces with normal structure / J. Math. Anal. Appl 104(1):285~292
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