Intersection properties of balls in spaces of compact operators

Asvald Lima

Annales de l'institut Fourier (1978)

  • Volume: 28, Issue: 3, page 35-65
  • ISSN: 0373-0956

Abstract

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We study the connection between intersection properties of balls and the existence of large faces of the unit ball in Banach spaces. Hanner’s result that a real space has the 3.2 intersection property if an only if disjoint faces of the unit ball are contained in parallel hyperplanes is extended to infinite dimensional spaces. It is shown that the space of compact operators from a space X to a space Y has the 3.2 intersection property if and only if X and Y have the 3.2 intersection property and either X or Y * is isometric to an L 1 ( μ ) -space.

How to cite

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Lima, Asvald. "Intersection properties of balls in spaces of compact operators." Annales de l'institut Fourier 28.3 (1978): 35-65. <http://eudml.org/doc/74375>.

@article{Lima1978,
abstract = {We study the connection between intersection properties of balls and the existence of large faces of the unit ball in Banach spaces. Hanner’s result that a real space has the 3.2 intersection property if an only if disjoint faces of the unit ball are contained in parallel hyperplanes is extended to infinite dimensional spaces. It is shown that the space of compact operators from a space $X$ to a space $Y$ has the 3.2 intersection property if and only if $X$ and $Y$ have the 3.2 intersection property and either $X$ or $Y^*$ is isometric to an $L_1(\mu )$-space.},
author = {Lima, Asvald},
journal = {Annales de l'institut Fourier},
language = {eng},
number = {3},
pages = {35-65},
publisher = {Association des Annales de l'Institut Fourier},
title = {Intersection properties of balls in spaces of compact operators},
url = {http://eudml.org/doc/74375},
volume = {28},
year = {1978},
}

TY - JOUR
AU - Lima, Asvald
TI - Intersection properties of balls in spaces of compact operators
JO - Annales de l'institut Fourier
PY - 1978
PB - Association des Annales de l'Institut Fourier
VL - 28
IS - 3
SP - 35
EP - 65
AB - We study the connection between intersection properties of balls and the existence of large faces of the unit ball in Banach spaces. Hanner’s result that a real space has the 3.2 intersection property if an only if disjoint faces of the unit ball are contained in parallel hyperplanes is extended to infinite dimensional spaces. It is shown that the space of compact operators from a space $X$ to a space $Y$ has the 3.2 intersection property if and only if $X$ and $Y$ have the 3.2 intersection property and either $X$ or $Y^*$ is isometric to an $L_1(\mu )$-space.
LA - eng
UR - http://eudml.org/doc/74375
ER -

References

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