Exponential dichotomy and strongly stable vectors of Hilbert space contraction semigroups

Authors

  • Nhan Levan Department of Electrical Engineering, University of California in Los Angeles, Los Angeles, CA 90024-1594, USA Author
  • Carlos S. Kubrusly Catholic University of Rio de Janeiro, 22453-900, Rio de Janeiro, RJ, Brazil Author

Keywords:

Exponential stability, strong stability, exponential dichotomy, strong dichotomy

Subjects:

47D03, 47A45

Abstract

The paper deals with exponential dichotomy and its relationship withstrongly stable vectors associated with Hilbert space semigroups.Contraction semigroups are decomposed by using the strongly stabilityoperator associated with the semigroup. Necessary and sufficientconditions for exponential stability and non-exponential stability areinvestigated in terms of norm inequalities—instead of a Lyapunovoperator equation.

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Published

2013-04-15

Issue

Vol. 65 No. 2 (2013): Vol. 65, Issue 2

Section

Articles

License

Copyright (c) 2013 Authors retain copyright to their work.

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.