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Mappings onto multiplicative subsets of function algebras and spectral properties of their products

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Arkiv för Matematik

Abstract

We characterize mappings S i and T i , not necessarily linear, from sets \(\mathcal {J}_{i}\), i=1,2, onto multiplicative subsets of function algebras, subject to the following conditions on the peripheral spectra of their products: σ π (S 1(a)S 2(b))⊂σ π (T 1(a)T 2(b)) and σ π (S 1(a)S 2(b))∩σ π (T 1(a)T 2(b))≠∅, \(a\in \mathcal {J}_{1}\), \(b\in \mathcal {J}_{2}\). As a direct consequence we obtain a large number of previous results about mappings subject to various spectral conditions.

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Authors and Affiliations

  1. Department of Mathematics Faculty of Science, Niigata University, Niigata, 950-2181, Japan

    Takeshi Miura

  2. Department of Mathematical Sciences, University of Montana, Missoula, MT, 59812, U.S.A.

    Thomas Tonev

Authors
  1. Takeshi Miura
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  2. Thomas Tonev
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Correspondence to Takeshi Miura.

Additional information

Dedicated to Junzo Wada.

The first author was supported by KAKENHI Grant Number 23740097.

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Miura, T., Tonev, T. Mappings onto multiplicative subsets of function algebras and spectral properties of their products. Ark Mat 53, 329–358 (2015). https://doi.org/10.1007/s11512-014-0210-y

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  • DOI: https://doi.org/10.1007/s11512-014-0210-y

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