Premium
Property (quasi‐ α ) and the denseness of norm attaining mappings
Author(s) -
Choi Yun Sung,
Song Hyun Gwi
Publication year - 2008
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200510676
Subject(s) - mathematics , property (philosophy) , tensor product , norm (philosophy) , banach space , pure mathematics , discrete mathematics , philosophy , epistemology , political science , law
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)