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  • Bulletin of the Australian Mathematical Society, Volume 77, Issue 3
  • June 2008, pp. 425-432

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

  • FRANCISCO J. GARCÍA-PACHECO (a1)
  • DOI: http://dx.doi.org/10.1017/S0004972708000348
  • Published online: 01 June 2008
Abstract
Abstract

An example is found of a nonreflexive Banach space X such that the union of {0} and the set of non-norm-attaining functionals on X contains no two-dimensional subspace.

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[3]R. M. Aron , V. I. Gurariy and J. B. Seoane-Sepúlveda , ‘Lineability and spaceability of sets of functions on ℝ’, Proc. Amer. Math. Soc. 133 (2005), 795803.

[4]R. M. Aron , D. Pérez-García and J. B. Seoane-Sepúlveda , ‘Algebrability of the set of non-convergent Fourier series’, Studia Math. 175 (2006), 8390.

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[6]F. Bayart , ‘Linearity of sets of strange functions’, Michigan Math. J. 53 (2005), 291303.

[7]F. Bayart and L. Quarta , ‘Algebras in sets of queer functions’, Israel J. Math 158 (2007), 285296.

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[11]F. J. García-Pacheco , N. Palmberg and J. B. Seoane-Sepúlveda , ‘Lineability and algebrability of pathological phenomena in analysis’, J. Math. Anal. Appl. 326 (2007), 929939.

[13]V. I. Gurariy and L. Quarta , ‘On lineability of sets of continuous functions’, J. Math. Anal. Appl. 294 (2004), 6272.

[14]R. C. James , ‘Bases and reflexivity of Banach spaces’, Ann. Math. 52 (1950), 518527.

[15]R. C. James , ‘A non-reflexive Banach space which is isomorphic to its second conjugate’, Proc. Natl. Acad. Sci. USA 37 (1951), 174177.

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Bulletin of the Australian Mathematical Society
  • ISSN: 0004-9727
  • EISSN: 1755-1633
  • URL: /core/journals/bulletin-of-the-australian-mathematical-society
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