Covering the Unit Sphere of Certain Banach Spaces by Sequences of Slices and Balls
Canadian mathematical bulletin, Tome 57 (2014) no. 1, pp. 42-50
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We prove that, given any covering of any infinite-dimensional Hilbert space $H$ by countably many closed balls, some point exists in $H$ which belongs to infinitely many balls. We do that by characterizing isomorphically polyhedral separable Banach spaces as those whose unit sphere admits a point-finite covering by the union of countably many slices of the unit ball.
Mots-clés :
46B20, 46C05, 52C17, point finite coverings, slices, polyhedral spaces, Hilbert spaces
Fonf, Vladimir P.; Zanco, Clemente. Covering the Unit Sphere of Certain Banach Spaces by Sequences of Slices and Balls. Canadian mathematical bulletin, Tome 57 (2014) no. 1, pp. 42-50. doi: 10.4153/CMB-2012-027-7
@article{10_4153_CMB_2012_027_7,
author = {Fonf, Vladimir P. and Zanco, Clemente},
title = {Covering the {Unit} {Sphere} of {Certain} {Banach} {Spaces} by {Sequences} of {Slices} and {Balls}},
journal = {Canadian mathematical bulletin},
pages = {42--50},
year = {2014},
volume = {57},
number = {1},
doi = {10.4153/CMB-2012-027-7},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2012-027-7/}
}
TY - JOUR AU - Fonf, Vladimir P. AU - Zanco, Clemente TI - Covering the Unit Sphere of Certain Banach Spaces by Sequences of Slices and Balls JO - Canadian mathematical bulletin PY - 2014 SP - 42 EP - 50 VL - 57 IS - 1 UR - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2012-027-7/ DO - 10.4153/CMB-2012-027-7 ID - 10_4153_CMB_2012_027_7 ER -
%0 Journal Article %A Fonf, Vladimir P. %A Zanco, Clemente %T Covering the Unit Sphere of Certain Banach Spaces by Sequences of Slices and Balls %J Canadian mathematical bulletin %D 2014 %P 42-50 %V 57 %N 1 %U http://geodesic.mathdoc.fr/articles/10.4153/CMB-2012-027-7/ %R 10.4153/CMB-2012-027-7 %F 10_4153_CMB_2012_027_7
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