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Bull. Korean Math. Soc. 2012; 49(1): 99-107
Printed January 1, 2012
https://doi.org/10.4134/BKMS.2012.49.1.99
Copyright © The Korean Mathematical Society.
Applications of Hilbert space dissipative norm
Carlos S. Kubrusly and Nhan Levan
Catholic University of Rio de Janeiro, University of California in Los Angeles
The concept of Hilbert space dissipative norm was introduced in [8] to obtain necessary and sufficient conditions for exponential stability of contraction semigroups. In the present paper we show that the same concept can also be used to derive further properties of contraction semigroups, as well as to characterize strongly stable semigroups that are not exponentially stable.
Keywords: Hilbert space contraction semigroups, dissipative norm and stabilities
MSC numbers: 47D03, 47A30
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