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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Isometric isomorphisms between Banach algebras related to locally compact groups
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by F. Ghahramani, A. T. Lau and V. Losert PDF
Trans. Amer. Math. Soc. 321 (1990), 273-283 Request permission

Abstract:

Let ${G_1}$, ${G_2}$ be locally compact groups. We prove in this paper that if $T$ is an isometric isomorphism from the Banach algebra ${\text {LUC}}{({G_1})^*}$ (the continuous dual of the Banach space of left uniformly continuous functions on ${G_1}$, equipped with Arens multiplication) onto ${\text {LUC}}{({G_2})^*}$, then $T$ maps $M({G_1})$ onto $M({G_2})$ and ${L^1}({G_1})$ onto ${L^1}({G_2})$. We also prove that any isometric isomorphism from ${L^1}{({G_1})^{**}}$ (second conjugate algebra of ${L^1}({G_1})$) onto ${L^1}{({G_2})^{**}}$ maps ${L^1}({G_1})$ onto ${L^1}({G_2})$.
References
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Additional Information
  • © Copyright 1990 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 321 (1990), 273-283
  • MSC: Primary 43A20; Secondary 43A10, 46J99
  • DOI: https://doi.org/10.1090/S0002-9947-1990-1005079-2
  • MathSciNet review: 1005079