Numerical index of vector-valued function spaces

Miguel Martín; Rafael Payá

Studia Mathematica (2000)

  • Volume: 142, Issue: 3, page 269-280
  • ISSN: 0039-3223

Abstract

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We show that the numerical index of a c 0 -, l 1 -, or l ∞ -sum of Banach spaces is the infimum of the numerical indices of the summands. Moreover, we prove that the spaces C(K,X) and L 1 ( μ , X ) (K any compact Hausdorff space, μ any positive measure) have the same numerical index as the Banach space X. We also observe that these spaces have the so-called Daugavet property whenever X has the Daugavet property.

How to cite

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Martín, Miguel, and Payá, Rafael. "Numerical index of vector-valued function spaces." Studia Mathematica 142.3 (2000): 269-280. <http://eudml.org/doc/216803>.

@article{Martín2000,
abstract = {We show that the numerical index of a $c_0$-, $l_1$-, or $l_∞$-sum of Banach spaces is the infimum of the numerical indices of the summands. Moreover, we prove that the spaces C(K,X) and $L_1(μ,X)$ (K any compact Hausdorff space, μ any positive measure) have the same numerical index as the Banach space X. We also observe that these spaces have the so-called Daugavet property whenever X has the Daugavet property.},
author = {Martín, Miguel, Payá, Rafael},
journal = {Studia Mathematica},
keywords = {numerical index; Daugavet property; sum of Banach spaces; vector-valued function space; numerical radius},
language = {eng},
number = {3},
pages = {269-280},
title = {Numerical index of vector-valued function spaces},
url = {http://eudml.org/doc/216803},
volume = {142},
year = {2000},
}

TY - JOUR
AU - Martín, Miguel
AU - Payá, Rafael
TI - Numerical index of vector-valued function spaces
JO - Studia Mathematica
PY - 2000
VL - 142
IS - 3
SP - 269
EP - 280
AB - We show that the numerical index of a $c_0$-, $l_1$-, or $l_∞$-sum of Banach spaces is the infimum of the numerical indices of the summands. Moreover, we prove that the spaces C(K,X) and $L_1(μ,X)$ (K any compact Hausdorff space, μ any positive measure) have the same numerical index as the Banach space X. We also observe that these spaces have the so-called Daugavet property whenever X has the Daugavet property.
LA - eng
KW - numerical index; Daugavet property; sum of Banach spaces; vector-valued function space; numerical radius
UR - http://eudml.org/doc/216803
ER -

References

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