Search results for "Fixed point property"

MR2595826 (2011c:46026) Domínguez Benavides, T. The Szlenk index and the fixed point property under renorming. Fixed Point Theory Appl. 2010, Art. ID…

2010

It is known that not every Banach space can be renormed so that the resultant space satisfies the weak Fixed Point Property (w-FPP). In the paper under review the author gives a further contribution to identify classes of Banach spaces which can be renormed to satisfy the w-FPP. Let $X$ be a Banach space and $X^*$ its dual. The dual norm is $UKK^*$ if for every $\varepsilon >0$ there is $\theta(\varepsilon)>0$ such that every $u$ in the closed unit ball $B_{X^*}$ of $X^*$ with $\|u\| > 1 - \theta(\varepsilon)$ has a weak$^*$ open neighborhood $\mathcal{U}$ with diam$(B_{X^*}\cap\mathcal{U})< \epsilon$. In [Bull. Lond. Math. Soc. 42 (2010), no. 2, 221--228; MR2601548] M. Raya showed that if …