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arXiv · 2102.09755

Property($K^*$) Implies $R(X) \leq 1 + \frac{\displaystyle 1}{\displaystyle 1 + r_{X^*}(1)}$

Tim Dalby
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Abstract

It is shown that if the dual of a Banach space satisfies Property($K^*$) then $R(X) \leq 1 + \frac{\displaystyle 1}{\displaystyle 1 + r_{X^*}(1)} < 2$ where $r_{X^*}(c)$ is Opial's modulus for $X^*.$ Thus $X$ has the weak fixed point property.

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Tim Dalby. 2021-02-19. Property($K^*$) Implies $R(X) \leq 1 + \frac{\displaystyle 1}{\displaystyle 1 + r_{X^*}(1)}$. https://arxiv.org/abs/2102.09755

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