Numerical index of absolute sums of Banach spaces

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:375

Article

Martin, Miguel¹  Meri, Javier¹  Popov, Mikhail²  Randrianantoanina, Beata³ 

[1] Univ Granada, Fac Ciencias, Dept Anal Matemat, E-18071 Granada, Spain

[2] Chernivtsi Natl Univ, Dept Math, UA-58012 Chernovtsy, Ukraine

[3] Miami Univ, Dept Math, Oxford, OH 45056 USA

关键词: Banach space;    Numerical index;    L(p)-space;    Absolute sum;    Kothe space;   

DOI  :  10.1016/j.jmaa.2010.08.061

来源: Elsevier

【 摘 要 】

We study the numerical index of absolute sums of Banach spaces, giving general conditions which imply that the numerical index of the sum is less or equal than the infimum of the numerical indices of the summands and we provide some examples where the equality holds covering the already known case of c(0)-, l(1-) and l(infinity)-sums and giving as a new result the case of E-sums where E has the RNP and n(E) = 1 (in particular for finite-dimensional E with n(E) = 1). We also show that the numerical index of a Banach space Z which contains a dense union of increasing one-complemented subspaces is greater or equal than the limit superior of the numerical indices of those subspaces. Using these results, we give a detailed short proof of the already known fact that, for a fixed p, the numerical indices of all infinite-dimensional L(p)(mu)-spaces coincide. (C) 2010 Elsevier Inc. All rights reserved.

【 授权许可】

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