Factorization of Almost Periodic Matrix Functions of Several Variables and Toeplitz Operators

Abstract

We study connections between operator theoretic properties of Toeplitz operators acting on suitable Besikovitch spaces and factorizations of their symbols which are matrix valued almost periodic functions of several real variables. Among other things, we establish the existence of a twisted canonical factorization for locally sectorial symbols, and characterize one-sided invertibility of Toeplitz operators in terms of their symbols. In addition, we study stability of factorizations, and factorizations of hermitian valued almost periodic matrix functions of several variables.