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Integral operators on spaces of continuous vector-valued functions


Author: Paulette Saab
Journal: Proc. Amer. Math. Soc. 111 (1991), 1003-1013
MSC: Primary 47B38; Secondary 46E40, 46G10, 47B10
DOI: https://doi.org/10.1090/S0002-9939-1991-1039263-5
MathSciNet review: 1039263
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Abstract: Let $ X$ be a compact Hausdorff space, let $ E$ be a Banach space, and let $ C(X,E)$ stand for the Banach space of $ E$-valued continuous functions on $ X$ under the uniform norm. In this paper we characterize integral operators (in the sense of Grothendieck) on $ C(X,E)$ spaces in terms of their representing vector measures. This is then used to give some applications to nuclear operators on $ C(X,E)$ spaces.


References [Enhancements On Off] (What's this?)

  • [1] G. Alexander, Linear operators on the space of vector-valued continuous functions, Ph.D. thesis, New Mexico State University, Las Cruces, New Mexico, 1972.
  • [2] R. Bilyeu and P. Lewis, Some mapping properties of representing measures, Ann. Math. Pure Appl. 109 (1976), 273-287. MR 0425609 (54:13563)
  • [3] G. Choquet, Lecture on analysis, Vol. II, Benjamin, New York, 1969.
  • [4] J. Diestel and J. J. Uhl, Jr., Vector measures, Math. Surveys 15 Amer. Math. Soc., Providence, RI, 1977. MR 0453964 (56:12216)
  • [5] N. Dinculeanu, Vector measures, Pergamon, Press, 1967. MR 0206190 (34:6011b)
  • [6] A. Grothendieck, Produits tensoriels topologiques et espaces nucléaires, Memoirs Amer. Math. Soc. 16 (1955), 1-140. MR 0075539 (17:763c)
  • [7] P. Saab, Integral representation by boundary vector measures, Canad. Math. Bull. 25 (1982), 164-168. MR 663609 (83j:46049)
  • [8] B. Smith, Some bounded linear operators on the spaces $ C(\Omega ,E)$ and $ A(K,E)$, Ph.D. thesis, University of Missouri, Columbia, MO, 1989.
  • [9] C. Swartz, Absolutely summing and dominated operators on spaces of vector valued continuous functions, Trans. Amer. Math. Soc. 179 (1973), 123-132. MR 0320796 (47:9330)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1991-1039263-5
Article copyright: © Copyright 1991 American Mathematical Society

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