The notion of the frame of the unit ball of Banach spaces was introduced to construct a new calculation method for the Dunkl-Williams constant. In this paper, we characterize the frame of the unit ball by using k-extreme points and extreme points of the unit ball of two-dimensional subspaces. Furthermore, we show that the frame of the unit ball is always closed, and is connected if the dimension of the space is not less than three. As infinite dimensional examples, the frame of the unit balls of c 0 and ℓ p are determined.
@article{bwmeta1.element.doi-10_2478_s11533-014-0437-7,
author = {Ryotaro Tanaka},
title = {On the frame of the unit ball of Banach spaces},
journal = {Open Mathematics},
volume = {12},
year = {2014},
pages = {1700-1713},
zbl = {1311.46019},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-014-0437-7}
}
Ryotaro Tanaka. On the frame of the unit ball of Banach spaces. Open Mathematics, Tome 12 (2014) pp. 1700-1713. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-014-0437-7/
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