151 research outputs found
Compressions of Resolvents and Maximal Radius of Regularity
Suppose that is left-invertible in for all , where is an open subset of the complex plane. Then an
operator-valued function is a left resolvent of in if
and only if has an extension , the resolvent of which is a
dilation of of a particular form. Generalized resolvents exist on
every open set , with included in the regular domain of . This
implies a formula for the maximal radius of regularity of in terms of the
spectral radius of its generalized inverses. A solution to an open problem
raised by J. Zem\'anek is obtained.Comment: 15 pages, to appear in Trans. Amer. Math. So
Metric and homogeneous structure of closed range operators
Let CR be the set of all bounded linear operators between Hilbert spaces H, K with closed range. This paper is devoted to the study of the topological properties of CR if certain natural metrics are considered on it. We also define an action of the group GH × GK on CR and determine the orbits of this action. These orbits, which are strongly related to the connected components for the topology defined by the metrics mentioned above, determine a stratification of the set of Fredholm and semi-Fredholm operators. Finally, we calculate the distance, with respect to some of the metrics mentioned above, between different orbits of CR.Fil: Corach, Gustavo. Consejo Nacional de Investigaciones CientÃficas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; ArgentinaFil: Maestripieri, Alejandra Laura. Consejo Nacional de Investigaciones CientÃficas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; ArgentinaFil: Mbekhta, Mostafa. Universite Lille; Franci
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