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A WEAKLY ANALYTIC LOCALLY CONVEX SPACE WHICH IS NOT K-ANALYTIC

  • JUAN CARLOS FERRANDO (a1)
Abstract
Abstract

It is shown that the dual of the space Cp(I) of all real-valued continuous functions on the closed unit interval with the pointwise topology, when equipped with the Mackey topology, is a non K-analytic but weakly analytic locally convex space.

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This research has been partially supported by project MTM2005-01182 of the Spanish Ministry of Education and Science, co-financed by the European Community (Feder funds).

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References
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[1] Arkhangel’skii A. V., Topological Function Spaces, Mathematics and its Applications, 78 (Kluwer Academic Publishers, Dordrecht, Boston, London, 1992).
[2] Ka̧kol J., López Pellicer M. and Śliwa W., Weakly K-analytic spaces and the three-space property for analyticity, submitted.
[3] Nakamura M., ‘On quasi-Souslin space and closed graph theorem’, Proc. Japan. Acad. 46 (1970).
[4] Rogers C. A., ‘Analytic sets in Hausdorff spaces’, Mathematika 11 (1968), 18.
[5] Talagrand M., ‘Espaces de Banach faiblement K-analytiques’, Ann. of Math. 110 (1979), 407438.
[6] Valdivia M., Topics in Locally Convex Spaces, North Holland Mathematics Studies, 67 (North Holland, Amsterdam, 1982).
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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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