Products of uniformly noncreasy spaces

Abstract

Abstract. We show that finite products of uniformly noncreasy spaces with a strictly monotone norm have the fixed point property for nonexpansive mappings. It gives new and natural examples of superreflexive Banach spaces without normal structure but with the fixed point property.

On the fixed point property in direct sums of Banach spaces with strictly monotone norms

“…Also, uniformly noncreasy spaces introduced in [45] are superreflexive and have FPP. Other examples of superreflexive Banach spaces without normal structure but with FPP are given by the results in [52,53].…”

The Fixed Point Property in Direct Sums and Modulus

“…Recall that Theorem 2.3 in [30] shows that the direct sum (X 1 ⊕... ⊕X r ) ψ of uniformly noncreasy spaces with a strictly monotone norm has FPP. Since uniformly noncreasy spaces are stable under passing to the Banach space ultrapowers (see [25]), the conclusion of Theorem 3.8 is also valid in this case.…”