On absolutely representing families of subspaces in Banach spaces

Abstract

An absolutely representing family of subspaces is a natural generalization of an absolutely representing system of subspaces and absolutely representing system (of elements). We obtain necessary an (or) sufficient conditions for a family of subspaces to be an absolutely representing family of subspaces and study properties of absolutely representing families of subspaces in Banach spaces. As an example, we study families of subspaces spanned by exponents.