On the Greatest Regular Closed Subalgebras and the Apostol Algebras of $L^p$-Multipliers Whose Fourier Transforms Are Continuous and Vanish at Infinity

Abstract

For certain algebras of continuous functions, the relationship between the greatest regular subalgebras, the algebras which consist of functions of which corresponding multiplication operators are decomposable, and the sets of functions with natural spectra are studied. In particular, spectral properties of certain Fourier multipliers are considered.