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 operator semigroups. This concerns in particular Markov semigroups in L 1 -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 L 1 -spaces. Related results, historical notes, exercises, and open problems accompany each chapter.

Presents in a systematic way recent results on the asymptotic behaviour of operator semigroups and related topics, especially concerning positive semigroups in classical and non-commutative L1-spaces Contains many open problems Includes supplementary material: sn.pub/extras

Inhalt
Elementary theory of one-parameter semigroups.- Positive semigroups in ordered Banach spaces.- Positive semigroups in L1-spaces.