ACTA issues

Maps preserving spectrally $n$-tuple multiplicative structures between function algebras

Rumi Shindo Togashi

Acta Sci. Math. (Szeged) 84:1-2(2018), 185-200

Abstract. Let $X$ and $Y$ be locally compact Hausdorff spaces, where $X$ is first-countable. Fix a positive integer $n \geq 3$ and a non-zero complex number $\lambda $. If a surjective map $T\colon C_{0}(X) \to C_{0}(Y)$ satisfies the condition $\sup _{y \in Y}\big |\big (\prod _{ k= 1}^{n}T(f_k)\big )(y)+\lambda \big | = \sup _{x \in X}\big |\big (\prod _{ k= 1}^{n}f_k \big )(x)+\lambda \big |$

DOI: 10.14232/actasm-017-076-5

AMS Subject Classification (1991): 46J10; 46H40, 46J20, 47B49

Keyword(s): function algebra, norm-preserving, peripheral spectrum, weighted composition operator

Received November 30, 2017 and in final form March 21, 2018. (Registered under 76/2017.)