Orthogonal systems in $L^2$ spaces of a vector measure

Abstract

Let m : Σ → X be a Banach space valued countably additive vector measure. In this paper we present a procedure to construct an m -orthogonal system in the space L 2 (m) of square integrable functions with respect to m .If the vector measure is constructed from a family of indeterminate scalar measures, it is possible to obtain a family of polynomials that is orthogonal with respect to this vector measure. On the other hand, if the vector measure is fixed, then we can obtain sequences of orthogonal functions using the Kadec − P elczyński disjointification method.