Tyshkevich D. On orthogonalization of systems of vectors and Wold decomposition in linear inner product spaces

Objects: linear inner product spaces and linear operators on them. Goals: development and generalization of well-known methods of investigation of linear operators on Hilbert or Krein spaces for the case of general inner product spaces. Methods: methods of linear algebra, functional analysis, topology, set theory, category theory. New theoretical results: theorem on existing of constructive procedure of orthogonalization of countable vector system is obtained; in the case of a reflexive regular Banach space the criterion of existing of Wold decomposition of a semiunutary operator is obtained; notion of a category with quadratic decomposition is introduced, theorem of existing of an elementary rotation of an operator from the same category is proved; description of all maximal reducing subspaces, on which a linear operator is unitary, is obtained Employment: the results are important for constructing of models for linear operators in general indefinite inner product spaces.