Displaying similar documents to “An operator inequality.”

Elements of C*-algebras commuting with their Moore-Penrose inverse

J. Koliha (2000)

Studia Mathematica

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We give new necessary and sufficient conditions for an element of a C*-algebra to commute with its Moore-Penrose inverse. We then study conditions which ensure that this property is preserved under multiplication. As a special case of our results we recover a recent theorem of Hartwig and Katz on EP matrices.

Mixed-type reverse order law and its equivalents

Nebojša Č. Dinčić, Dragan S. Djordjević, Dijana Mosić (2011)

Studia Mathematica

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We present new results related to various equivalents of the mixed-type reverse order law for the Moore-Penrose inverse for operators on Hilbert spaces. Recent finite-dimensional results of Tian are extended to Hilbert space operators.

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...

Operator matrix of Moore-Penrose inverse operators on Hilbert C*-modules

Mehdi Mohammadzadeh Karizaki, Mahmoud Hassani, Maryam Amyari, Maryam Khosravi (2015)

Colloquium Mathematicae

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We show that the Moore-Penrose inverse of an operator T is idempotent if and only if it is a product of two projections. Furthermore, if P and Q are two projections, we find a relation between the entries of the associated operator matrix of PQ and the entries of associated operator matrix of the Moore-Penrose inverse of PQ in a certain orthogonal decomposition of Hilbert C*-modules.

Convergence of Rump's method for computing the Moore-Penrose inverse

Yunkun Chen, Xinghua Shi, Yi Min Wei (2016)

Czechoslovak Mathematical Journal

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We extend Rump's verified method (S. Oishi, K. Tanabe, T. Ogita, S. M. Rump (2007)) for computing the inverse of extremely ill-conditioned square matrices to computing the Moore-Penrose inverse of extremely ill-conditioned rectangular matrices with full column (row) rank. We establish the convergence of our numerical verified method for computing the Moore-Penrose inverse. We also discuss the rank-deficient case and test some ill-conditioned examples. We provide our Matlab codes for...

On generalized inverses in C*-algebras

Robin Harte, Mostafa Mbekhta (1992)

Studia Mathematica

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We investigate when a C*-algebra element generates a closed ideal, and discuss Moore-Penrose and commuting generalized inverses.

Continuity of generalized inverses in Banach algebras

Steffen Roch, Bernd Silbermann (1999)

Studia Mathematica

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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.

An extension of invertibility of Hammerstein-type operators

Radu Tunaru (1999)

Czechoslovak Mathematical Journal

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My aim is to show that some properties, proved to be true for the square matrices, are true for some not necessarily linear operators on a linear space, in particular, for Hammerstein-type operators.