• Corpus ID: 16710320

On Nicely Smooth Banach Spaces

  title={On Nicely Smooth Banach Spaces},
  author={Pradipta Bandyopadhyay and Sudeshna Basu},
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… 
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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:


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