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2 results

  • An ordered suprabarrelled space

  • Part of
  • J. C. Ferrando, M. López-Pellicer
  • Journal:
    Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics / Volume 51 / Issue 1 / August 1991
    Published online by Cambridge University Press:
    09 April 2009, pp. 106-117
    Print publication:
    August 1991
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  • A locally convex space E is said to be ordered suprabarrelled if given any increasing sequence of subspaces of E covering E there is one of them which is suprabarrelled. In this paper we show that the space m0(X, Σ), where X is any set and Σ is a σ-algebra on X, is ordered suprabarrelled, given an affirmative answer to a previously raised question. We also include two applications of this result to the theory of vector measures.

  • On the Pták homomorphism theorem

  • Part of
  • B. Rodrigues
  • Journal:
    Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics / Volume 47 / Issue 2 / October 1989
    Published online by Cambridge University Press:
    09 April 2009, pp. 322-333
    Print publication:
    October 1989
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  • In this note, a brief and accessible proof is given of an extension of the Pták homomorphism theorem to a larger class of spaces—spaces that are not necessarily assumed to be locally convex. This is done by first proving a counterpart of the Bourbaki-Grothendieck homomophism theorem for the non-locally-convex case. Our presentation utilizes the simplifying properties of seminorms.