Isometries of $L^ 1\cap L^ p$
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- Proc. Amer. Math. Soc. 93 (1985), 493-496 Request permission
Abstract:
Denote by ${L^1} \cap {L^p}$ the Banach space of all functions $f$ such that $f \in {L^1}$ and $f \in {L^p}$ with norm $|||f||| = \max (||f|{|_1},||f|{|_p})$. We give a characterization of isometries of ${L^1} \cap {L^p}$ and show that $T$ is an isometry if and only if $T$ is of the form $Tf = h\Phi (f)$, where $\Phi$ is an operator generated by a regular set isomorphism and $h$ is a suitable function.References
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Additional Information
- © Copyright 1985 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 93 (1985), 493-496
- MSC: Primary 46E30; Secondary 47B38
- DOI: https://doi.org/10.1090/S0002-9939-1985-0774009-4
- MathSciNet review: 774009