Menchoff-Rademacher type theorems in vector-valued Banach function spaces

Abstract

We present a simple procedure which transfers classical coefficient tests on summation of orthonormal series in $L_2(\mu)$ into theorems on summation for unconditionally convergent series in vector-valued Banach function spaces $E(X)$ (where $E$ is a Banach function space over a measure space $(\Omega, \mu)$ and $X$ a Banach space).