# On the frame of the unit ball of Banach spaces

Open Mathematics (2014)

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

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topRyotaro 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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