A generalized Banach–Stone theorem for C0(K,X) spaces via the modulus of convexity of X⁎

We shall introduce a new geometric constant C Z ( λ , μ , X ) {C}_{Z}\left(\lambda ,\mu ,X) based on a generalization of the parallelogram law, which was proposed by Moslehian and Rassias. First, it is shown that, for a Banach space, C Z ( λ , μ , X ) {C}_{Z}\left(\lambda ,\mu ,X) is equal to 1 if and only if the norm is induced by an inner product. Next, a characterization of uniformly non-square is given, that is, X X has the fixed point property. Also, a sufficient condition which implies weak normal structure is presented. Moreover, a generalized James constant J ( λ , X ) J\left(\lambda ,X) is also introduced. Finally, some basic properties of this new coefficient are presented.

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Geometric Constants in Banach Spaces Related to the Inscribed Quadrilateral of Unit Balls

Ahmad

Liu

2021

Symmetry

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We introduce a new geometric constant Jin(X) based on a generalization of the parallelogram law, which is symmetric and related to the length of the inscribed quadrilateral side of the unit ball. We first investigate some basic properties of this new coefficient. Next, it is shown that, for a Banach space, Jin(X) becomes 16 if and only if the norm is induced by an inner product. Moreover, its properties and some relations between other well-known geometric constants are studied. Finally, a sufficient condition which implies normal structure is presented.

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A generalized Banach–Stone theorem for C0(K,X) spaces via the modulus of convexity of X⁎

Cited by 4 publications

References 18 publications

On New Moduli Related to the Generalization of the Parallelogram Law

On New Moduli Related to the Generalization of the Parallelogram Law

Some aspects of generalized Zbăganu and James constant in Banach spaces

Geometric Constants in Banach Spaces Related to the Inscribed Quadrilateral of Unit Balls

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