Displaying similar documents to “On continuity of the Moore-Penrose and Drazin inverses.”

On the generalized Drazin inverse and generalized resolvent

Dragan S. Djordjević, Stanimirović, Predrag S. (2001)

Czechoslovak Mathematical Journal

Similarity:

We investigate the generalized Drazin inverse and the generalized resolvent in Banach algebras. The Laurent expansion of the generalized resolvent in Banach algebras is introduced. The Drazin index of a Banach algebra element is characterized in terms of the existence of a particularly chosen limit process. As an application, the computing of the Moore-Penrose inverse in C * -algebras is considered. We investigate the generalized Drazin inverse as an outer inverse with prescribed range...

Continuity of the Drazin inverse II

J. Koliha, V. Rakočević (1998)

Studia Mathematica

Similarity:

We study the continuity of the generalized Drazin inverse for elements of Banach algebras and bounded linear operators on Banach spaces. This work extends the results obtained by the second author on the conventional Drazin inverse.

Continuity of generalized inverses in Banach algebras

Steffen Roch, Bernd Silbermann (1999)

Studia Mathematica

Similarity:

The main topic of the paper is the continuity of several kinds of generalized inversion of elements in a Banach algebra with identity. We introduce the notion of asymptotic generalized invertibility and completely characterize sequences of elements with this property. Based on this result, we derive continuity criteria which generalize the well known criteria from operator theory.

Explicit solutions of infinite linear systems associated with group inverse endomorphisms

Fernando Pablos Romo (2022)

Czechoslovak Mathematical Journal

Similarity:

The aim of this note is to offer an algorithm for studying solutions of infinite linear systems associated with group inverse endomorphisms. As particular results, we provide different properties of the group inverse and we characterize EP endomorphisms of arbitrary vector spaces from the coincidence of the group inverse and the Moore-Penrose inverse.