The Adjoint Of A Semigroup Of Linear Operators

This monograph provides a systematic treatment of the abstract theory of adjoint semigroups. After presenting the basic elementary results, the following topics are treated in detail: The sigma (X, X )-topology, -reflexivity, the Favard class, Hille-Yosida operators, interpolation and extrapolation, weak -continuous semigroups, the codimension of X in X , adjoint semigroups and the Radon-Nikodym property, tensor products of semigroups and duality, positive semigroups and multiplication semigroups. The major part of the material is reasonably self-contained and is accessible to anyone with basic knowledge of semi- group theory and Banach space theory. Most of the results are proved in detail. The book is addressed primarily to researchers working in semigroup theory, but in view of the "Banach space theory" flavour of many of the results, it will also be of interest to Banach space geometers and operator theorists.

Advanced graduate-level treatment of semigroup theory explores semigroups of linear operators and linear Cauchy problems. The text features challenging exercises and emphasizes motivation, heuristics, and further applications. 1985 edition.

This book presents a systematic account of the theory of asymptotic behaviour of semigroups of linear operators acting in a Banach space. The focus is on the relationship between asymptotic behaviour of the semigroup and spectral properties of its infinitesimal generator. The most recent developments in the field are included, such as the Arendt-Batty-Lyubich-Vu theorem, the spectral mapp- ing theorem of Latushkin and Montgomery-Smith, Weis's theorem on stability of positive semigroup in Lp-spaces, the stability theorem for semigroups whose resolvent is bounded in a half-plane, and a systematic theory of individual stability. Addressed to researchers and graduate students with interest in the fields of operator semigroups and evolution equations, this book is self-contained and provides complete proofs.

Provides a graduate-level introduction to the theory of semigroups of operators.

Since the characterization of generators of C0 semigroups was established in the 1940s, semigroups of linear operators and its neighboring areas have developed into an abstract theory that has become a necessary discipline in functional analysis and differential equations. This book presents that theory and its basic applications, and the last two chapters give a connected account of the applications to partial differential equations.

The book offers a direct and up-to-date introduction to the theory of one-parameter semigroups of linear operators on Banach spaces. The book is intended for students and researchers who want to become acquainted with the concept of semigroups.