Abstract
A necessary and sufficient condition for exponential stability of Hilbert space contraction semigroups is obtained in terms of an inequality involving the dissipative norm associated with the generator of the semigroup and with the Hilbert space norm.
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Boyadzhiev, K.N., Levan, N.: Strong stability of Hilbert space contraction semigroups. Stud. Sci. Math. Hung. 30, 165–182 (1995)
Chill, R., Tomilov, Y.: Stability of operator semigroups: ideas and results. Perspectives in Operator Theory (Banach Cent. Publ., Pol. Acad. Sci., Warsaw) 75, 71–109 (2007)
Datko, R.: Extending a theorem of A.M. Liapunov to Hilbert space. J. Math. Anal. Appl. 32, 610–616 (1970)
Datko, R.: Uniform asymptotic stability of evolutionary process in a Banach space. SIAM J. Math. Anal. 3, 428–445 (1972)
Fillmore, P.A.: Notes on Operator Theory. Van Nostrand, Princeton (1970)
Kubrusly, C.S., Levan, N.: Proper contractions and invariant subspaces. Int. J. Math. Math. Sci. 28, 223–230 (2001)
Kubrusly, C.S., Vieira, P.C.M.: Strong stability for cohyponormal operators. J. Oper. Theory 31, 123–127 (1994)
Lax, P.D., Phillips, R.S.: Scattering Theory. Academic Press, San Diego (1967)
Sz.-Nagy, B., Foiaş, C.: Harmonic Analysis of Operators on Hilbert Space. North-Holland, Amsterdam (1970)
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Communicated by Jerome A. Goldstein.
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Kubrusly, C.S., Levan, N. Stabilities of Hilbert space contraction semigroups revisited. Semigroup Forum 79, 341–348 (2009). https://doi.org/10.1007/s00233-009-9134-4
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DOI: https://doi.org/10.1007/s00233-009-9134-4