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- W1566649078 abstract "Let X be a Banach space, $X_2 subseteq X$ be a two dimensional subspace of $X$, and $S(X) = {x in X, ||x|| = 1}$ be the unit sphere of $X$. The relationship between the normal structure and the arc length in X is studied. Let $R(X) = mbox{inf} {l(S(X_2)) - gamma(X_22) : X_2 subseteq X}$, where $l(S(X_2))$ is the circumference of $S(X_2)$ and $gamma(X_2) = mbox{sup}{2(||x + y|| + ||x - y||) : x; y in S(X_2)}$ is the least upper bound of the perimeters of the inscribed parallelogram of $S(X_2)$. The main result is that $R(X) gt 0$ implies $X$ has the uniform normal structure." @default.
- W1566649078 created "2016-06-24" @default.
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- W1566649078 date "2001-06-01" @default.
- W1566649078 modified "2023-10-18" @default.
- W1566649078 title "NORMAL STRUCTURE AND THE ARC LENGTH IN BANACH SPACES" @default.
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- W1566649078 doi "https://doi.org/10.11650/twjm/1500407342" @default.
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