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Proceedings of the American Mathematical Society

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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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  • [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
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DOI: https://doi.org/10.1090/S0002-9939-1984-0735571-X
Article copyright: © Copyright 1984 American Mathematical Society