On the Characteristic Operators and Projections and on the Solutions of Weyl Type of Dissipative and Accumulative Operator Systems. II. Abstract Theory

Анотація

Special maximal semi-definite subspaces (maximal dissipative and accumulative relations) are considered. Particular cases of those arise in studying boundary problems for systems mentioned in the title. We provide a description of such subspaces and list their properties. A criterion is found that condition of semi-definiteness of sum of indefinite quadratic forms reduces to semi-definiteness of each of the summand forms, i.e it is separated. In the case when the forms depend on a parameter $\lambda$ (e.g., a spectral parameter) within a domain $\Lambda \subset \mathbb{C}$, a condition is found under which separation of the semi-definiteness property at a single $\lambda$ implies its separation for all $\lambda$.

Mathematics Subject Classification: 34B07, 34G10, 46C20, 47A06, 47B50.