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- W2062733679 abstract "Letr, s ∈ [0, 1], and let X be a Banach space satisfying the M(r, s)-inequality, that is, $parallel x^{***} parallel geqslant rparallel pi _X x^{***} parallel + sparallel x^{***} - pi _X x^{***} parallel for x^{***} in X^{***} ,$ where πX is the canonical projection from X*** onto X*. We show some examples of Banach spaces not containing c0, having the point of continuity property and satisfying the above inequality for r not necessarily equal to one. On the other hand, we prove that a Banach space X satisfying the above inequality for s=1 admits an equivalent locally uniformly rotund norm whose dual norm is also locally uniformly rotund. If, in addition, X satisfies $mathop {lim sup }limits_alpha parallel u^* + sx_alpha ^* parallel leqslant mathop {lim sup }limits_alpha parallel v^* + x_alpha ^* parallel $ whenever u*, v* ∈X* with ‖u*‖≤‖v*‖ and (x ${}_{α}^{*}$ ) is a bounded weak* null net in X*, then X can be renormed to satisfy the, M(r, 1) and the M(1, s)-inequality such that X* has the weak* asymptotic-norming property I with respect to BX." @default.
- W2062733679 created "2016-06-24" @default.
- W2062733679 creator A5012307346 @default.
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- W2062733679 date "2002-10-01" @default.
- W2062733679 modified "2023-09-27" @default.
- W2062733679 title "On M-structure, the asymptotic-norming property and locally uniformly rotund renormings" @default.
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- W2062733679 doi "https://doi.org/10.1007/bf02384539" @default.
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