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A $ v$-integral representation for linear operators on a space of continuous vector-valued functions


Authors: J. R. Edwards and S. G. Wayment
Journal: Proc. Amer. Math. Soc. 30 (1971), 260-262
MSC: Primary 47.25; Secondary 28.00
DOI: https://doi.org/10.1090/S0002-9939-1971-0281030-1
MathSciNet review: 0281030
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Abstract | References | Similar Articles | Additional Information

Abstract: In this note an analytic representation is given for continuous linear operators from $ C(X)$ into a linear normed space Y where $ C(X)$ is the space of continuous functions on [0, 1] with values in a linear normed space X.


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

  • [1] J. R. Edwards and S. G. Wayment, Representation for transformations continuous in the BV norm, Trans. Amer. Math. Soc. 154 (1971), 251-265. MR 0274704 (43:466)
  • [2] D. H. Tucker, A note on the Riesz representation theorem, Proc. Amer. Math. Soc. 14 (1963), 354-358. MR 26 #2865. MR 0145334 (26:2865)
  • [3] -, A representation theorem for a continuous linear transformation on a space of continuous functions, Proc. Amer. Math. Soc. 16 (1965), 946-953. MR 33 #7865. MR 0199722 (33:7865)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1971-0281030-1
Keywords: Continuous linear operator, vector-valued function, representation theorem, convex-Gowurin, v-integral, polygonal function
Article copyright: © Copyright 1971 American Mathematical Society

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