Про деякі властивості оператора Грама
Year: 2025
Type: article
Abstract: UDC 512.552.4 The $G$-construction allows us to obtain a system of subspaces using an abstract Gram operator. Any system of subspaces is unitarily equivalent to a system constructed by using this method. We propose another construction of a system of subspaces with the same property, provide criteria for the unitary equivalence of a pair of systems of subspaces in terms of the corresponding Gram operators, and study the problem of irreducibility of a system of subspaces in terms of the corresponding Gram operator. In addition, we provide an example illustrating how the obtained results apply to the study of a certain class of the systems of subspaces.
Author: Олександр Стрілець
Institution: Institute of Mathematics
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4410191022