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October 2015 Mappings onto multiplicative subsets of function algebras and spectral properties of their products
Takeshi Miura, Thomas Tonev
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Ark. Mat. 53(2): 329-358 (October 2015). DOI: 10.1007/s11512-014-0210-y

Abstract

We characterize mappings Si and Ti, 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: σπ(S1(a)S2(b))⊂σπ(T1(a)T2(b)) and σπ(S1(a)S2(b))∩σπ(T1(a)T2(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.

Funding Statement

The first author was supported by KAKENHI Grant Number 23740097.

Dedication

Dedicated to Junzo Wada.

Citation

Download Citation

Takeshi Miura. Thomas Tonev. "Mappings onto multiplicative subsets of function algebras and spectral properties of their products." Ark. Mat. 53 (2) 329 - 358, October 2015. https://doi.org/10.1007/s11512-014-0210-y

Information

Received: 25 April 2014; Published: October 2015
First available in Project Euclid: 30 January 2017

zbMATH: 1335.46044
MathSciNet: MR3391175
Digital Object Identifier: 10.1007/s11512-014-0210-y

Rights: 2015 © Institut Mittag-Leffler

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Vol.53 • No. 2 • October 2015
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