SOLUTION OF NORMALLY SOLVABLE OPERATOR EQUATIONS IN A HILBERT SPACE

摘要

We find a formula for the unique pseudoinverse of a normally solvable operator, establish conditions for the existence of a unique solution of a normally solvable equation, and obtain its representation in a Hilbert space. We also introduce the notion of one-sided pseudoinverse operators for normally solvable operators acting in Hilbert spaces and consider methods for their construction.