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Stability of Operators and Operator Semigroups

  • Tanja Eisner
Book

Part of the Operator Theory: Advances and Applications book series (OT, volume 209)

Table of contents

  1. Front Matter
    Pages i-xi
  2. Tanja Eisner
    Pages 5-35
  3. Tanja Eisner
    Pages 37-77
  4. Tanja Eisner
    Pages 79-132
  5. Tanja Eisner
    Pages 133-162
  6. Tanja Eisner
    Pages 163-182
  7. Back Matter
    Pages 183-204

About this book

Introduction

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.

Keywords

Group theory dynamical systems stability

Authors and affiliations

  • Tanja Eisner
    • 1
  1. 1.Arbeitsbereich FunktionalanalysisMathematisches InstitutTübingenGermany

Bibliographic information