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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.

Intrinsic geometric on the class of probability densities and exponential families.

Henryk Gzyl, Lázaro Recht (2007)

Publicacions Matemàtiques

We present a way of thinking of exponential farnilies as geodesic surfaces in the class of positive functions considered as a (multiplicative) sub-group G+ of the group G of all invertible elements in the algebra A of all complex bounded functions defined on a measurable space. For that we have to study a natural geometry on that algebra. The class D of densities with respect to a given rneasure will happen to be representatives of equivalence classes defining a projective space in A. The natural...

Invariant metrics on convex cones

Edoardo Vesentini (1976)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Invariant Subspaces of Compact Elements in C*-Algebras.

M.R.F. Smyth, T.T. West (1977)

Mathematische Zeitschrift

Invariante Spuren auf Gruppenalgebren.

Fritz Mayer-Lindenberg (1979)

Journal für die reine und angewandte Mathematik

Invarianz gewisser Operatorenklassen unter nichtkommutativen ergodischen Mitteln.

Jürgen Tischer, Hans Wittmer (1974)

Manuscripta mathematica

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

Julio Benítez, Vladimir Rakočević (2010)

Studia Mathematica

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.

Invertibility-preserving maps of $C^{*}$ -algebras with real rank zero.

Kovacs, Istvan (2005)

Abstract and Applied Analysis

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