Orthogonal systems in L2 spaces of a vector measure

Let m:S \to 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 L2(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-Pelczynski disjointification method.

Anahtar Kelimeler:

Orthogonal sequences, vector measures, integration

Orthogonal systems in L2 spaces of a vector measure

Keywords:

Orthogonal sequences, vector measures, integration,

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