Displaying similar documents to “Integral representations of the g -Drazin inverse in C * -algebras”

Differentiability of the g-Drazin inverse

J. J. Koliha, V. Rakočević (2005)

Studia Mathematica

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If A(z) is a function of a real or complex variable with values in the space B(X) of all bounded linear operators on a Banach space X with each A(z)g-Drazin invertible, we study conditions under which the g-Drazin inverse A ( z ) is differentiable. From our results we recover a theorem due to Campbell on the differentiability of the Drazin inverse of a matrix-valued function and a result on differentiation of the Moore-Penrose inverse in Hilbert spaces.

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...

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.

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 .

Identification of a localized source in an interstellar cloud: an inverse problem

Meri Lisi, Silvia Totaro (2005)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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We study an inverse problem for photon transport in an interstellar cloud. In particular, we evaluate the position x 0 of a localized source q ⁢ x = q 0 ⁢ δ ⁢ x - x 0 , inside a nebula (for example, a star). We assume that the photon transport phenomenon is one-dimensional. Since a nebula moves slowly in time, the number of photons U inside the cloud changes slowly in time. For this reason, we consider the so-called quasi-static approximation u to the exact solution U . By using semigroup theory, we prove existence...

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...