Journal Article

POLYNOMIAL NUMERICAL INDEX FOR SOME COMPLEX VECTOR-VALUED FUNCTION SPACES

Yun Sung Choi, Domingo García, Manuel Maestre and Miguel Martín

in The Quarterly Journal of Mathematics

Volume 59, issue 4, pages 455-474
Published in print December 2008 | ISSN: 0033-5606
Published online January 2008 | e-ISSN: 1464-3847 | DOI: https://dx.doi.org/10.1093/qmath/ham054
POLYNOMIAL NUMERICAL INDEX FOR SOME COMPLEX VECTOR-VALUED FUNCTION SPACES

Show Summary Details

Preview

We study the relation between the polynomial numerical indices of a complex vector-valued function space and the ones of its range space. It is proved that the spaces C(K, X) and L(μ, X) have the same polynomial numerical index as the complex Banach space X for every compact Hausdorff space K and every σ-finite measure μ, which does not hold any more in the real case. We give an example of a complex Banach space X such that, for every k ≥ 2, the polynomial numerical index of order k of X is the greatest possible, namely 1, while the one of X** is the least possible, namely kk/(1−k). We also give new examples of Banach spaces with the polynomial Daugavet property, namely L(μ, X) when μ is atomless, and Cw(K, X), Cw*(K, X*) when K is perfect.

Journal Article.  0 words. 

Subjects: Pure Mathematics

Full text: subscription required

How to subscribe Recommend to my Librarian

Users without a subscription are not able to see the full content. Please, subscribe or login to access all content. subscribe or login to access all content.