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1997 | 66 | 1 | 263-268
Tytuł artykułu

On a property of weak resolvents and its application to a spectral problem

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Abstrakty
EN
We show that the poles of a resolvent coincide with the poles of its weak resolvent up to their orders, for operators on Hilbert space which have some cyclic properties. Using this, we show that a theorem similar to the Mlak theorem holds under milder conditions, if a given operator and its adjoint have cyclic vectors.
Twórcy
  • Department of Mathematics and Computer Science, Adam Mickiewicz University, Matejki 48/49, 60-769 Poznań, Poland
Bibliografia
  • [1] H. R. Dowson, Spectral Theory of Linear Operators, Academic Press, London, 1978.
  • [2] N. Dunford and J. T. Schwartz, Linear Operators, Part I: General Theory, Intescience, New York, 1958.
  • [3] C. K. Fong, E. A. Nordgren, H. Radjavi and P. Rosenthal, Weak resolvents of linear operators, II, Indiana Univ. Math. J. 39 (1990), 67-83.
  • [4] J. W. Helton, Discrete time systems, operator models, and scattering theory, J. Funct. Anal. 16 (1974), 15-38.
  • [5] J. W. Helton, Systems with infinite-dimensional state space: the Hilbert space approach, Proc. IEEE 64 (1976), 145-160.
  • [6] P. Jakóbczak and J. Janas, On Nikolski theorem for several operators, Bull. Polish Acad. Sci. Math. 31 (1983), 369-374.
  • [7] J. Janas, On a theorem of Lebow and Mlak for several commuting operators, Studia Math. 76 (1983), 249-253.
  • [8] T. Kailath, Linear Systems, Prentice-Hall, Englewood Cliffs, N.J., 1980.
  • [9] R. E. Kalman, P. L. Falb and M. A. Arbib, Topics in Mathematical System Theory, McGraw-Hill, New York, 1969.
  • [10] T. Kato, Perturbation Theory for Linear Operators, 2nd ed., Springer, Berlin, 1976.
  • [11] P. D. Lax and R. S. Phillips, Scattering Theory, rev. ed., Academic Press, New York, 1989.
  • [12] A. Lebow, Spectral radius of an absolutely continuous operator, Proc. Amer. Math. Soc. 36 (1972), 511-514.
  • [13] W. Mlak, On a theorem of Lebow, Ann. Polon. Math. 35 (1977), 107-109.
  • [14] N. K. Nikol'skiĭ, A Tauberian theorem on the spectral radius, Sibirsk. Mat. Zh. 18 (1977), 1367-1372 (in Russian).
  • [15] E. Nordgren, H. Radjavi and P. Rosenthal, Weak resolvents of linear operators, Indiana Univ. Math. J. 36 (1987), 913-934.
  • [15] W. Rudin, Real and Complex Analysis, 2nd ed., McGraw-Hill, New York, 1974.
  • [16] B. Sz.-Nagy and C. Foiaş, Harmonic Analysis of Operators on Hilbert Space, North-Holland, Amsterdam, 1970.
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Bibliografia
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bwmeta1.element.bwnjournal-article-apmv66z1p263bwm
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