DOI QR코드

DOI QR Code

APPLICATIONS OF HILBERT SPACE DISSIPATIVE NORM

  • Kubrusly, Carlos S. (Catholic University of Rio de Janeiro) ;
  • Levan, Nhan (Department of Electrical Engineering University of California in Los Angeles)
  • 투고 : 2010.06.29
  • 발행 : 2012.01.31

초록

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.

참고문헌

  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. https://doi.org/10.1016/0022-247X(70)90283-0
  4. R. Datko, Uniform asymptotic stability of evolutionary process in a Banach space, SIAM J. Math. Anal. 3 (1972), 428-445. https://doi.org/10.1137/0503042
  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. https://doi.org/10.1155/S0161171201006287
  8. C. S. Kubrusly and N. Levan, Stabilities of Hilbert space contraction semigroups revisited, Semigroup Forum 79 (2009), no. 2, 341-348. https://doi.org/10.1007/s00233-009-9134-4
  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. https://doi.org/10.1109/TCS.1978.1084539
  11. B. Sz.-Nagy and C. Foias, Harmonic Analysis of Operators on Hilbert Space, North-Holland, Amsterdam, 1970.