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Asplund Operators on Locally Convex Spaces

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Proceedings of the Second ISAAC Congress

Abstract

We study the relationship between the local Radon-Nikodým property, introduced by Defant [4] as a generalization of the Radon-Nikodým property to duals of locally convex spaces, and the Asplund operators, introduced by Robertson [7]. We also give a characterization of Asplund symmetric tensor products of Banach spaces in terms of Asplund maps.

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References

  1. C. Boyd, S. Dineen, M. P. Rueda, Locally Asplund spaces of weakly uniformly continuous holomorphic functions. Preprint.

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  2. C. Boyd, S. Dineen, P. Rueda, Locally Asplund preduals of spaces of holomorphic functions. Preprint.

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  3. Choi, Kim, Polynomial properties of Banach spaces, J. Math. Anal. Appl. 190 (1995), 202–210.

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  4. Defant, The local Radon-Nikodým property for duals of locally convex spaces. Bulletin de la Société Royale des Sciencies de Liège. 53e année, 5, (1984), 233–246.

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  5. A. Defant, A duality theorem for locally convex tensor products. Math. Z., 190, (1985), 45–53.

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  6. J. Diestel, J. J. Uhl, Vector measures. Amer. Math. Soc. Mathematical Surveys, 15, (1977).

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  7. N. Robertson, Asplund operators and holomorphic maps. Manuscripta Math., 75, (1992), 25–34.

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  8. R. A. Ryan, Applications of topological tensor products to infinite dimensional holomorphy. Ph.D. Thesis. Dublin University, (1980).

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© 2000 Kluwer Academic Publishers

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Boyd, C., Dineen, S., Rueda, M.P. (2000). Asplund Operators on Locally Convex Spaces. In: Begehr, H.G.W., Gilbert, R.P., Kajiwara, J. (eds) Proceedings of the Second ISAAC Congress. International Society for Analysis, Applications and Computation, vol 8. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-0271-1_27

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  • DOI: https://doi.org/10.1007/978-1-4613-0271-1_27

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4613-7971-3

  • Online ISBN: 978-1-4613-0271-1

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