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Convex Functions on ``Sequentially Reflexive'' Banach Spaces

Borwein, Jonathan M. and Vanderwerff, Jon D. (1995) Convex Functions on ``Sequentially Reflexive'' Banach Spaces. [Preprint]

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      Abstract

      There is a sizeable class of results precisely relating boundedness, convergence and differentiability properties of continuous convex functions on Banach spaces to whether or not the space contains an isomorphic copy of $\ell_1$. In this note, we provide constructions showing that the main such results do not extend to natural broader classes of functions.

      Item Type: Preprint
      Additional Information: pubdom FALSE
      Subjects: 46-xx Functional analysis > 46Axx Topological linear spaces and related structures
      46-xx Functional analysis > 46Bxx Normed linear spaces and Banach spaces; Banach lattices
      52-xx Convex and discrete geometry > 52Axx General convexity
      Faculty: UNSPECIFIED
      Depositing User: Users 1 not found.
      Date Deposited: 17 Nov 2003
      Last Modified: 21 Apr 2010 11:13
      URI: https://docserver.carma.newcastle.edu.au/id/eprint/115

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