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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Notes on interpolation by the real method between $C(T,A_ 0)$ and $C(T,A_ 1)$
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by Mieczysław Mastyło PDF
Proc. Amer. Math. Soc. 102 (1988), 945-948 Request permission

Abstract:

Let $A$ be a Banach space and let $T$ be a compact Hausdorff space. We denote by $C(T,A)$ the Banach space of all $A$-valued continuous functions defined on $T$ endowed with the supremum norm. We show that if $T$ is infinite and $({A_0},{A_1})$ is a Banach couple with ${A_0}$ continuously embedded in ${A_1}$, then the interpolation space ${(C(T,{A_0}),C(T,{A_1}))_{\varphi ,p}}$ is equal to $C\left ( {T,{{\left ( {{A_0},{A_1}} \right )}_{\varphi ,p}}} \right )$ if and only if ${A_0}$ is closed in ${A_1}$.
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Additional Information
  • © Copyright 1988 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 102 (1988), 945-948
  • MSC: Primary 46E40; Secondary 46M35
  • DOI: https://doi.org/10.1090/S0002-9939-1988-0934872-3
  • MathSciNet review: 934872