Bulletin of the Australian Mathematical Society

Research Article

VECTOR SUBSPACES OF THE SET OF NON-NORM-ATTAINING FUNCTIONALS

FRANCISCO J. GARCÍA-PACHECOa1

a1 Department of Mathematical Sciences, Kent State University, Kent, OH 44242, USA (email: fgarcia@math.kent.edu)

Abstract

An example is found of a nonreflexive Banach space X such that the union of {0} and the set $X^*\setminus \mathsf {NA}(X)$ of non-norm-attaining functionals on X contains no two-dimensional subspace.

(Received August 15 2007)

2000 Mathematics subject classification

  • 46B20;
  • 46B03;
  • 46B07

Keywords and phrases

  • lineable;
  • non-norm-attaining functional;
  • James space

Footnotes

This paper is dedicated to Professor Richard M. Aron