English

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

Functional Analysis 2022-06-22 v2

Abstract

It is shown that if the dual of a Banach space satisfies Property(KK^*) then R(X)1+11+rX(1)<2R(X) \leq 1 + \frac{\displaystyle 1}{\displaystyle 1 + r_{X^*}(1)} < 2 where rX(c)r_{X^*}(c) is Opial's modulus for X.X^*. Thus XX has the weak fixed point property.

Keywords

Cite

@article{arxiv.2102.09755,
  title  = {Property($K^*$) Implies $R(X) \leq 1 + \frac{\displaystyle 1}{\displaystyle 1 + r_{X^*}(1)}$},
  author = {Tim Dalby},
  journal= {arXiv preprint arXiv:2102.09755},
  year   = {2022}
}

Comments

arXiv admin note: text overlap with arXiv:2007.00942