On the frame of the unit ball of Banach spaces

Ryotaro Tanaka

Open Mathematics (2014)

  • Volume: 12, Issue: 11, page 1700-1713
  • ISSN: 2391-5455

Abstract

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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.

How to cite

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Ryotaro Tanaka. "On the frame of the unit ball of Banach spaces." Open Mathematics 12.11 (2014): 1700-1713. <http://eudml.org/doc/269791>.

@article{RyotaroTanaka2014,
abstract = {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.},
author = {Ryotaro Tanaka},
journal = {Open Mathematics},
keywords = {k-extreme point; Exposed face; Frame; -extreme point; exposed face; frame of the unit ball of Banach spaces},
language = {eng},
number = {11},
pages = {1700-1713},
title = {On the frame of the unit ball of Banach spaces},
url = {http://eudml.org/doc/269791},
volume = {12},
year = {2014},
}

TY - JOUR
AU - Ryotaro Tanaka
TI - On the frame of the unit ball of Banach spaces
JO - Open Mathematics
PY - 2014
VL - 12
IS - 11
SP - 1700
EP - 1713
AB - 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.
LA - eng
KW - k-extreme point; Exposed face; Frame; -extreme point; exposed face; frame of the unit ball of Banach spaces
UR - http://eudml.org/doc/269791
ER -

References

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