Displaying similar documents to “Differentiability of the g-Drazin inverse”

Invertibility of the commutator of an element in a C*-algebra and its Moore-Penrose inverse

Julio Benítez, Vladimir Rakočević (2010)

Studia Mathematica

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We study the subset in a unital C*-algebra composed of elements a such that a a † - a a † is invertible, where a † denotes the Moore-Penrose inverse of a. A distinguished subset of this set is also investigated. Furthermore we study sequences of elements belonging to the aforementioned subsets.

Inverse Sequences and Absolute Co-Extensors

Ivan Ivanšić, Leonard R. Rubin (2007)

Bulletin of the Polish Academy of Sciences. Mathematics

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Suppose that K is a CW-complex, X is an inverse sequence of stratifiable spaces, and X = limX. Using the concept of semi-sequence, we provide a necessary and sufficient condition for X to be an absolute co-extensor for K in terms of the inverse sequence X and without recourse to any specific properties of its limit. To say that X is an absolute co-extensor for K is the same as saying that K is an absolute extensor for X, i.e., that each map f:A → K from a closed subset A of X extends...

Linear inessential operators and generalized inverses

Bruce A. Barnes (2009)

Commentationes Mathematicae Universitatis Carolinae

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The space of inessential bounded linear operators from one Banach space X into another Y is introduced. This space, I ( X , Y ) , is a subspace of B ( X , Y ) which generalizes Kleinecke’s ideal of inessential operators. For certain subspaces W of I ( X , Y ) , it is shown that when T ∈ B ( X , Y ) has a generalized inverse modulo W , then there exists a projection P ∈ B ( X ) such that T ( I - P ) has a generalized inverse and T P ∈ W .

On the generalized Drazin inverse and generalized resolvent

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

Czechoslovak Mathematical Journal

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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...

Separation axioms, covering properties, and inverse limits generated by developable topological spaces

Harald Brandenburg

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CONTENTSIntroduction.............................................................................5Notation..................................................................................8§1. The spaces D and D 1 ................................................9§2. D-completely regular spaces..........................................15§3. On the epireflective hull of Moore spaces.......................24§4. D-normal spaces.............................................................29§5....

Integral representations of the g -Drazin inverse in C * -algebras

N. Castro González, Jaromír J. Koliha, Yi Min Wei (2004)

Mathematica Bohemica

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The paper gives new integral representations of the g -Drazin inverse of an element a of a C * -algebra that require no restriction on the spectrum of a . The representations involve powers of a and of its adjoint.