Konzistentnost i problemi kompletiranja operatorskih matrica: doktorske disertacije

Abstract

In this thesis different types of operator matrix completions have been studied, as well as consistency in invertibility and in Fredholmnes. The property consistency has been considered on Banach algebras in the sense of concsistency in invertibility and consistence in Fredholmnes. Result concering completions of operator matrices are linked to certain properties of a linear combination of two arbitrary Hilbert space operators. The properties studied in this thesis are: invertibility, injectivity, left (right) invertibility, closednes of range, consistency in invertibility of a linear combination of two arbitrary Hilbert space operators. Some of these results are applied to the study of the Generalized Bott-Duffin inverse, primarily to represent the Generalized Bott-Duffin inverse of bounded linear operator on a Hilbert space using an operator matrix. The obtained operator matrix representation of the Generalized Bott-Duffin inverse is a generalization of previous results.