One-parameter semigroups of positive operators. (English) Zbl 0585.47030

Lecture Notes in Mathematics. 1184. Berlin etc.: Springer-Verlag. X, 460 p. DM 64.00 (1986).

This book contains a complete and exhaustive treatment of the whole theory subsumable under the title of the book. More precisely the three subjects
(i) ”Characterization of the generator of semigroups having special properties (such as the positivity preserving property)”,
(ii) ”Spectral theory”, and
(iii) ”Asymptotic behaviour of semigroups”
are treated in various settings such as Banach spaces, Banach lattices, Spaces of type \(C_ 0(X)\), and Operator algebras.
The book contains the most recent and important results in this field. Thus it is indispensable for further research.

Reviewer: M.Wolff

MSC:

47D03	Groups and semigroups of linear operators
47-02	Research exposition (monographs, survey articles) pertaining to operator theory
47B60	Linear operators on ordered spaces
47-06	Proceedings, conferences, collections, etc. pertaining to operator theory
00Bxx	Conference proceedings and collections of articles
46B42	Banach lattices
34G10	Linear differential equations in abstract spaces
47C15	Linear operators in \(C^*\)- or von Neumann algebras

Keywords:

differential equations in Banach spaces; generator of semigroups; positivity preserving; Spectral theory; Asymptotic behaviour of semigroups; Banach spaces; Banach lattices; Spaces of type \(C_ 0(X)\); Operator algebras