Reduction of the Gram Operator for Some Classes of the Systems of Subspaces
摘要
In the investigation of systems of subspaces with given conditions imposed on the pairs of subspaces, we encounter the problem of nonnegativity of the associated Gram operator. We prove a theorem that enables us to reduce this problem, for some classes of subspaces, to the problem of nonnegativity of the Gram operator for a “smaller” system of subspaces.