Displaying similar documents to “The λ -function in the space P ( 2 ℓ 2 2 ) .”

Boundedness of linear maps

T. S. S. R. K. Rao (2000)

Commentationes Mathematicae Universitatis Carolinae

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In this short note we consider necessary and sufficient conditions on normed linear spaces, that ensure the boundedness of any linear map whose adjoint maps extreme points of the unit ball of the domain space to continuous linear functionals.

On the frame of the unit ball of Banach spaces

Ryotaro Tanaka (2014)

Open Mathematics

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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...

On the lambda-property and computation of the lambda-function of some normed spaces.

Mohamed Akkouchi, Hassan Sadiky (1993)

Extracta Mathematicae

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R. M. Aron and R. H. Lohman introduced, in [1], the notion of lambda-property in a normed space and calculated the lambda-function for some classical normed spaces. In this paper we give some more general remarks on this lambda-property and compute the lambda-function of other normed spaces, namely: B(S,∑,X) and M(E).

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

Hiroyasu Mizuguchi, Kichi-Suke Saito, Ryotaro Tanaka (2013)

Open Mathematics

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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∞.