Local spectrum of a family of operators

Abstract: Starting from the classic definitions of local resolvent set and spectrum of a linear bounded operator on a Banach space, we introduce the local resolvent set and spectrum, the local space and the single-valued extention property of a family of linear bounded operators on a Banach space. Keeping the analogy with the classic case, we extend some the known results from the case of a linear bouded operator to the case of a family of linear bounded operators on a Banach space.