Journal of Operator Theory

Volume 58, Issue 2, Fall 2007 pp. 229-250.

The real linear resolvent and cosolvent operators

Authors: Marko Huhtanen (1) and Olavi Nevanlinna (2)
Author institution: (1) Institute of Mathematics, Helsinki University of Technology, Box 1100, FIN-02015, Finland
(2) Institute of Mathematics, Helsinki University of Technology, Box 1100, FIN-02015, Finland

Summary: For an

$\setR$ -linear operator

$\oper{A}$ the resolvent operator is defined outside the spectrum of

$\oper{A}$ while the cosolvent operator is defined outside the proper values of

$\oper{A}$ . In this paper these two functions are studied. Series expansions are given. A new characterization for the eigenvalues of real matrices is obtained. The cosolvent operator is used to define and analyze analytic functions of

$\oper{A}$ . An application of this leads to a decomposition of

$\setR$ -linear operators. Classes of structured

$\setR$ -linear operators are considered.

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