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Compact homomorphisms between uniform Fréchet algebras

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Abstract

We study compact homomorphisms between uniform Fréchet algebras, by analyzing the behavior of its spectral adjoint on the underlying spectrum. We prove that every compact homomorphism between uniform Fréchet algebras actually ranges into a uniform Banach algebra, and that its spectral adjointmaps τ-bounded subsets into relatively τ-compact subsets, when τ is the strong or the compact-open topology.

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Authors and Affiliations

  1. Federal University of Pelotas, UFPel, São Paulo, Brazil

    Cicero Nachtigall

  2. University of São Paulo, São Paulo, SP, Brazil

    Daniela M. Vieira

Authors
  1. Cicero Nachtigall
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  2. Daniela M. Vieira
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Corresponding author

Correspondence to Daniela M. Vieira.

Additional information

Partially supported by CNPq, Brazil.

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Nachtigall, C., Vieira, D.M. Compact homomorphisms between uniform Fréchet algebras. Bull Braz Math Soc, New Series 47, 853–862 (2016). https://doi.org/10.1007/s00574-016-0192-4

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  • DOI: https://doi.org/10.1007/s00574-016-0192-4

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