# On Nicely Smooth Banach Spaces

@inproceedings{Bandyopadhyay1996OnNS, title={On Nicely Smooth Banach Spaces}, author={Pradipta Bandyopadhyay and Sudeshna Basu}, year={1996} }

We work with real Banach spaces. We will denote by B(X), S(X) and B[x, r] respectively the closed unit ball, the unit sphere and the closed ball of radius r > 0 around x ∈ X. We will identify any element x ∈ X with its canonical image in X∗∗. All subspaces we usually consider are norm closed. Definition 1.1. (a) We say A ⊆ B(X∗) is a norming set for X if ‖x‖ = sup{x∗(x) : x∗ ∈ A}, for all x ∈ X. A closed subspace F ⊆ X∗ is a norming subspace if B(F ) is a norming set for X. (b) A Banach space X…

## 4 Citations

A NOTE ON NORM ATTAINING FUNCTIONALS

- Mathematics
- 1998

We are concerned in this paper with the density of functionals which do not attain their norms in Banach spaces. Some earlier results given for separable spaces are extended to the nonseparable case.…

Big points in C*-algebras and JB*-triples

- Mathematics
- 2005

Let X be a Banach space. For a norm-one element u in X we put sðX; uÞ :¼ sup{jjc 2 PðcÞjj : c [ DðX pp ; uÞ}; where DðX pp ; ·Þ denotes the duality mapping of X pp , and P : X ppp ! X p stands for…

Very non-constrained subspaces of Banach spaces

- Mathematics
- 2003

Stat–Math Division, Indian Statistical Institute, 203, B.T. Road, Kolkata 700 108, India, e-mail: pradipta@isical.ac.in Department of Mathematics, Howard University, Washington DC 20059, USA, e-mail:…

## References

SHOWING 1-10 OF 28 REFERENCES

Spaces of compact operators

- Mathematics
- 1974

In this paper we study the structure of the Banach space K(E, F) of all compact linear operators between two Banach spaces E and F. We study three distinct problems: weak compactness in K(E, F),…

On the structure of non-dentable closed bounded convex sets

- Mathematics
- 1988

A self-contained proof is given of the following result.
Theorem. Let K be a non-dentable closed bounded convex nonempty subset of a Banach space X so that K equals the closed convex hull of its…

Characterisation of normed linear spaces with Mazur's intersection property

- MathematicsBulletin of the Australian Mathematical Society
- 1978

Normed linear spaces possessing the euclidean space property that every bounded closed convex set is an intersection of closed balls, are characterised as those with dual ball having weak* denting…

Renorming Banach spaces with the Mazur intersection property

- Mathematics
- 1997

In this paper we give new sufficient and necessary conditions for a Banach space to be equivalently renormed with the Mazur intersection property. As a consequence, several examples and applications…

Balls intersection properties of Banach spaces

- MathematicsBulletin of the Australian Mathematical Society
- 1992

Necessary and sufficient conditions for a Banach space with the Mazur intersection property to be an Asplund space are given. It is proved that Mazur intersection property is determined by the…

M-Ideals in Banach Spaces and Banach Algebras

- Mathematics
- 1993

Basic theory of M-ideals.- Geometric properties of M-ideals.- Banach spaces which are M-ideals in their biduals.- Banach spaces which are L-summands in their biduals.- M-ideals in Banach algebras.-…

Duality in spaces of operators and smooth norms on Banach spaces

- Mathematics
- 1988

On considere des espaces d'operateurs entre espaces de Banach et leur dualite. On etudie et on utilise le lien entre les proprietes metriques et de topologie faible des espaces de Banach

Smoothness and the asymptotic-norming properties of Banach spaces

- MathematicsBulletin of the Australian Mathematical Society
- 1992

We study some smoothness properties of a Banach space X that are related to the weak* asymptotic-norming properties of the dual space X*. These properties imply that X is an Asplund space and are…