Stability of Operators and Operator Semigroups

Download or read book Stability of Operators and Operator Semigroups written by Tanja Eisner and published by . This book was released on 2010 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.