Non-spectral Asymptotic Analysis of One-Parameter Operator Semigroups [electronic resource] /
Emel'yanov, Eduard Yu.author.
In this book, non-spectral methods are presented and discussed that have been developed over the last two decades for the investigation of asymptotic behavior of one-parameter operator semigroups in Banach spaces. This concerns in particular Markov semigroups in L1-spaces, motivated by applications to probability theory and dynamical systems. Recently many results on the asymptotic behaviour of Markov semigroups were extended to positive semigroups in Banach lattices with order-continuous norm, and to positive semigroups in non-commutative L1-spaces. Related results, historical notes, exercises, and open problems accompany each chapter. The book is directed to graduate students and researchers working in operator theory, particularly those interested in C0-semigroups in classical and non-commutative L1-spaces, in mean ergodic theory, and in dynamical systems.
Description based upon print version of record.
Includes bibliographical references (p. [159]-167) and index.
Elementary theory of one-parameter semigroups -- Positive semigroups in ordered Banach spaces -- Positive semigroups in L1-spaces.
In this book, non-spectral methods are presented and discussed that have been developed over the last two decades for the investigation of asymptotic behavior of one-parameter operator semigroups in Banach spaces. This concerns in particular Markov semigroups in L1-spaces, motivated by applications to probability theory and dynamical systems. Recently many results on the asymptotic behaviour of Markov semigroups were extended to positive semigroups in Banach lattices with order-continuous norm, and to positive semigroups in non-commutative L1-spaces. Related results, historical notes, exercises, and open problems accompany each chapter. The book is directed to graduate students and researchers working in operator theory, particularly those interested in C0-semigroups in classical and non-commutative L1-spaces, in mean ergodic theory, and in dynamical systems.
Operator theory.
Functional analysis.
Measure theory.
Operator Theory.
Functional Analysis.
Measure and Integration.

Operator theory