# MathSciDoc: An Archive for Mathematician ∫

#### Spectral Theory and Operator Algebramathscidoc:1701.32006

Arkiv for Matematik, 53, (2), 329-358, 2014.4
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.
@inproceedings{takeshi2014mappings,
title={Mappings onto multiplicative subsets of function algebras and spectral properties of their products},
author={Takeshi Miura, and Thomas Tonev},
url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203640771865085},
booktitle={Arkiv for Matematik},
volume={53},
number={2},
pages={329-358},
year={2014},
}

Takeshi Miura, and Thomas Tonev. Mappings onto multiplicative subsets of function algebras and spectral properties of their products. 2014. Vol. 53. In Arkiv for Matematik. pp.329-358. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203640771865085.