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The Lorentz space as a dual space

Author: Pratibha G. Ghatage
Journal: Proc. Amer. Math. Soc. 91 (1984), 92-94
MSC: Primary 46E30
MathSciNet review: 735571
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Abstract: If $ (X,S,\mu )$ is a finite, completely nonatomic measure space and $ \phi (t) = {t^{1/p}}(p > 1)$ then the Lorentz space $ {N_\phi }$ is the dual space of the closed span of simple functions in $ {M_\phi }( = N_\phi ^ * )$.

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  • [1] Nelson Dunford and Jacob T. Schwartz, Linear Operators. I. General Theory, With the assistance of W. G. Bade and R. G. Bartle. Pure and Applied Mathematics, Vol. 7, Interscience Publishers, Inc., New York; Interscience Publishers, Ltd., London, 1958. MR 0117523
  • [2] M. S. Steigerwalt and A. J. White, Some function spaces related to 𝐿_{𝑝} spaces, Proc. London Math. Soc. (3) 22 (1971), 137–163. MR 0279582
  • [3] Walter Rudin, Real and complex analysis, 2nd ed., McGraw-Hill Book Co., New York-Düsseldorf-Johannesburg, 1974. McGraw-Hill Series in Higher Mathematics. MR 0344043

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Article copyright: © Copyright 1984 American Mathematical Society