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Positive linear systems. - The method of positive operators - Transl. from the Russian by Jürgen Appell. (English) Zbl 0674.47036
Sigma Series in Applied Mathematics, 5. Berlin: Heldermann-Verlag. vii, 534 p. DM 88.00 (1989).

This nice book pursues a tradition of Soviet books on the subject and tries to fill a gap in the literature. It collects several results concerning spaces which are partially ordered by some cones and operators in ordered Banach spaces. Perhaps positivity is not always well known and used in full; the present book indicates several applications to (mainly linear) problems arising e.g. in system theory, mechanics and mathematics (spectral theory, numerical problems, forced oscillations in nonlinear systems, problems of stability and so on). Among these results, organized in the four chapters of the book, some were previously available only in research journals and/or in Russian; the list of references contains more than 200 entries.

The title of the four chapters are the following: basic notions; applications to spectral properties; applications to iteration procedures; other applications. Several exercises (of different difficulty, often containing facts of independent interest) are spread throughout the book. A selection of the material contained in the book can be used to teach a university course, to the advantage of students and teachers.

For the review of the original see Zbl 0578.47030.

Reviewer: P.L.Papini

47H07Monotone and positive operators on ordered topological linear spaces
46A40Ordered topological linear spaces, vector lattices
47-02Research monographs (operator theory)
47B60Operators on ordered spaces
46B42Banach lattices
47A10Spectrum and resolvent of linear operators