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
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
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