Property (quasi‐ α ) and the denseness of norm attaining mappings

We introduce property ( quasi ‐ α ), which implies property ( A ) defined by Lindenstrauss [10] and whose dual property is property (quasi‐ β ) [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‐ α ) and X n has property ( A ), then the projective tensor product X 1 ··· X n has property ( A ). (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)