Stability of Operators and Operator Semigroups

Description

This book is about stability of linear dynamical systems, discrete and continuous. More precisely, we discuss convergence to zero of strongly continuous semigroups of operators and of powers of a bounded linear operator, both with respect to different topologies. The discrete and the continuous cases are treated in parallel, and we systematically employ a comparison of methods and results in either case. Apart from classical results, many recent crucial developments in the area are presented, such as the resolvent approach to stability. Special attention is payed to stability with respect to the weak operator topology. We also connect stability in operator theory to its analogues in ergodic theory and harmonic analysis. The book is addressed to all researchers and graduate students interested in this field. Front Matter ....Pages i-xi Functional analytic tools (Tanja Eisner)....Pages 5-35 Stability of linear operators (Tanja Eisner)....Pages 37-77 Stability of C0-semigroups (Tanja Eisner)....Pages 79-132 Connections to ergodic and measure theory (Tanja Eisner)....Pages 133-162 Discrete vs. continuous (Tanja Eisner)....Pages 163-182 Back Matter ....Pages 183-204