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APPLICATIONS OF HILBERT SPACE DISSIPATIVE NORM
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 Title & Authors
APPLICATIONS OF HILBERT SPACE DISSIPATIVE NORM
Kubrusly, Carlos S.; Levan, Nhan;
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 Abstract
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;
 Language
English
 Cited by
 References
1.
K. N. Boyadzhiev and N. Levan, Strong stability of Hilbert space contraction semigroups, Studia Sci. Math. Hungar. 30 (1995), no. 3-4, 165-182.

2.
R. Chill and Y. Tomilov, Stability of operator semigroups: ideas and results, Perspectives in operator theory, 71-109, Banach Center Publ., 75, Polish Acad. Sci., Warsaw, 2007.

3.
R. Datko, Extending a theorem of A.M. Liapunov to Hilbert space, J. Math. Anal. Appl. 32 (1970), 610-616. crossref(new window)

4.
R. Datko, Uniform asymptotic stability of evolutionary process in a Banach space, SIAM J. Math. Anal. 3 (1972), 428-445. crossref(new window)

5.
P. A. Fillmore, Notes on Operator Theory, Van Nostrand, New York, 1970.

6.
J. A. Goldstein, Semigroups of Linear Operators and Applications, Oxford University Press, New York, 1985.

7.
C. S. Kubrusly and N. Levan, Proper contractions and invariant subspaces, Int. J. Math. Math. Sci. 28 (2001), no. 4, 223-230. crossref(new window)

8.
C. S. Kubrusly and N. Levan, Stabilities of Hilbert space contraction semigroups revisited, Semigroup Forum 79 (2009), no. 2, 341-348. crossref(new window)

9.
C. S. Kubrusly and P. C. M. Vieira, Strong stability for cohyponormal operators, J. Operator Theory 31 (1994), no. 1, 123-127.

10.
N. Levan, The stabilizability problem: a Hilbert space operator decomposition approach, IEEE Trans. Circuits and Systems 25 (1978), no. 9, 721-727. crossref(new window)

11.
B. Sz.-Nagy and C. Foias, Harmonic Analysis of Operators on Hilbert Space, North-Holland, Amsterdam, 1970.