Property (quasi-alpha) and the denseness of norm attaining mappings

Abstract

We introduce property (quasi-alpha), which implies property (A) defined by Lindenstrauss [10] and whose dual property is property (quasi-beta) [2]. We consider relations between this property and other sufficient conditions for property (A), and study the denseness of norm attaining mappings under the conditions of these properties. In particular, if each of the Banach spaces X-k, 1 <= k <= n - 1, has property (quasi-alpha) and X-n has property (A), then the projective tensor product X-1(circle times) over cap (pi) ... (circle times) over cap X-pi(n) has property (A). (C) 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.