On bases for direct decomposition

Аннотация

A method for constructing a basis for a Banach space from bases for its subspaces is proposed. The case of isomorphic subspace bases and the case when no corresponding isomorphisms are required are considered separately. The completeness, minimality, uniform minimality, and basis property with parentheses of the corresponding systems are studied. This approach has wide applications in the spectral theory of discontinuous differential operators.