Constantin Buse, Gul Rahmat
Let be a nondecreasing function which is positive on and let be a positive strongly continuous periodic evolution family of bounded linear operators acting on a complex Hilbert space . We prove that is uniformly exponentially stable if for each unit vector , one has
The result seems to be new and it generalizes others of the same topic. Moreover, the proof is surprisingly simple.
Submitted October 3, 2012. Published November 29, 2012.
Math Subject Classifications: 47A30, 46A30.
Key Words: Uniform exponential stability; Rolewicz's type theorems; weak integral stability boundedness.
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|Constantin Buse |
West University of Timisoara
Department of Mathematics
Bd. V. Parvan No. 4, 300223-Timisoara, Romania
| Gul Rahmat |
Government College University
Abdus Salam School of Mathematical Sciences
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