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On the frame of the unit ball of Banach spaces

100%

Tanaka R.

Open Mathematics

2014

tom 12

nr 11

1700-1713

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.

On the calculation of the Dunkl-Williams constant of normed linear spaces

51%

Mizuguchi H., Saito K.-S., Tanaka R.

Open Mathematics

2013

tom 11

nr 7

1212-1227

Recently, Jiménez-Melado et al. [Jiménez-Melado A., Llorens-Fuster E., Mazcuñán-Navarro E.M., The Dunkl-Williams constant, convexity, smoothness and normal structure, J. Math. Anal. Appl., 2008, 342(1), 298–310] defined the Dunkl-Williams constant DW(X) of a normed linear space X. In this paper we present some characterizations of this constant. As an application, we calculate DW(ℓ2-ℓ∞) in the Day-James space ℓ2-ℓ∞.

Ograniczanie wyników

2 Open Mathematics

2 Tanaka R.

1 Mizuguchi H.

1 Saito K.-S.

1 2014

1 2013

Wyniki wyszukiwania

On the frame of the unit ball of Banach spaces

On the calculation of the Dunkl-Williams constant of normed linear spaces