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How to solve an operator equation.

Martin Mathieu (1992)

Publicacions Matemàtiques

This article summarizes a series of lectures delivered at the Mathematics Department of the University of Leipzig, Germany, in April 1991, which were to overview techniques for solving operator equations on C*-algebras connected with methods developed in a Spanish-German research project on "Structure and Applications of C*-Algebras of Quotients" (SACQ). One of the researchers in this project was Professor Pere Menal until his unexpected death this April. To his memory this paper shall be dedicated....

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

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

Mathematica Bohemica

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...

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