Mathieu, Martin How to solve an operator equation. (English) Zbl 0791.46046 Publ. Mat., Barc. 36, No. 2B, 743-760 (1992). The author discusses the techniques for solving operator equations on \(C^*\)-algebras. The equations are of the form \(T_{\alpha, x_ 1,\dots,x_ n} =0\) where \(\alpha\) is a parameter and \(x_ 1,\dots, x_ n\) are unknowns in a \(C^*\)-algebra. There are examples involving derivations, completely positive operators, centralizing mappings and generators of dynamical semigroups. The main device for solving such equations is the so-called local multiplier algebra which provides a unified approach to the above examples. Reviewer: C.-h.Chu (London) MSC: 46L57 Derivations, dissipations and positive semigroups in \(C^*\)-algebras 46L05 General theory of \(C^*\)-algebras Keywords:operator equations on \(C^*\)-algebras; derivations; completely positive operators; centralizing mappings; generators of dynamical semigroups; local multiplier algebra PDFBibTeX XMLCite \textit{M. Mathieu}, Publ. Mat., Barc. 36, No. 2B, 743--760 (1992; Zbl 0791.46046) Full Text: DOI EuDML