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1992 | 103 | 1 | 17-24
Tytuł artykułu

On an estimate for the norm of a function of a quasihermitian operator

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Let A be a closed linear operator acting in a separable Hilbert space. Denote by co(A) the closed convex hull of the spectrum of A. An estimate for the norm of f(A) is obtained under the following conditions: f is a holomorphic function in a neighbourhood of co(A), and for some integer p the operator $A^p - (A*)^p$ is Hilbert-Schmidt. The estimate improves one by I. Gelfand and G. Shilov.
Czasopismo
Rocznik
Tom
103
Numer
1
Strony
17-24
Opis fizyczny
Daty
wydano
1992
otrzymano
1990-11-02
poprawiono
1991-04-24
poprawiono
1991-11-08
Twórcy
autor
  • Department of Mathematics, Ben Gurion University, P.O. Box 653, Beer Sheva 84105, Israel
Bibliografia
  • [1] N. I. Akhiezer and I. M. Glazman, Theory of Linear Operators in Hilbert Space, Nauka, Moscow 1966 (in Russian).
  • [2] L. de Branges, Some Hilbert spaces of analytic functions, J. Math. Anal. Appl. 12 (1965), 149-186.
  • [3] M. S. Brodskiǐ, Triangular and Jordan Representations of Linear Operators, Nauka, Moscow 1969 (in Russian); English transl.: Transl. Math. Monographs 32, Amer. Math. Soc., Providence, R.I., 1971.
  • [4] N. Dunford and J. T. Schwartz, Linear Operators, II. Spectral Theory, Selfadjoint Operators in Hilbert Space, Interscience, New York 1963.
  • [5] I. M. Gelfand and G. E. Shilov, Some Questions of the Theory of Differential Equations, Fiz.-Mat. Liter., Moscow 1958 (in Russian).
  • [6] M. I. Gil', On an estimate for the stability domain of differential systems, Differentsial'nye Uravneniya 19 (8) (1983), 1452-1454 (in Russian).
  • [7] M. I. Gil', On an estimate for the norm of a function of a Hilbert-Schmidt operator, Izv. Vyssh. Uchebn. Zaved. Mat. 1979 (8) (207), 14-19 (in Russian).
  • [8] M. I. Gil', On an estimate for the resolvents of nonselfadjoint operators "close" to selfadjoint and to unitary ones, Mat. Zametki 33 (1980), 161-167 (in Russian).
  • [9] I. Ts. Gokhberg and M. G. Kreǐn, Introduction to the Theory of Linear Nonselfadjoint Operators, Nauka, Moscow 1965 (in Russian); English transl.: Transl. Math. Monographs 18, Amer. Math. Soc., Providence, R.I., 1969.
  • [10] I. Ts. Gokhberg and M. G. Kreǐn, Theory and Applications of Volterra Operators in Hilbert Space, Nauka, Moscow 1967 (in Russian); English transl.: Transl. Math. Monographs 24, Amer. Math. Soc., Providence, R.I., 1970.
  • [11] D. Henry, Geometric Theory of Semilinear Parabolic Equations, Springer, Berlin 1981.
  • [12] T. Kato, Perturbation Theory for Linear Operators, Springer, Berlin 1966.
Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-smv103i1p17bwm
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