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Języki publikacji
Abstrakty
We prove a variant of Hildebrandt's theorem which asserts that the convex hull of the essential spectrum of an operator A on a complex Hilbert space is equal to the intersection of the essential numerical ranges of operators which are similar to A. As a consequence, it is given a necessary and sufficient condition for zero not being in the convex hull of the essential spectrum of A.
Słowa kluczowe
Czasopismo
Rocznik
Tom
Strony
279--285
Opis fizyczny
Bibliogr. 9 poz.
Twórcy
autor
- University ol Ljubljana, IMFM Jadranska ul. 19 SI-1000 Ljubljana Slovenia
autor
- Instituto Universitario de Lisboa Departamento de Matematica Av. das Forcas
Bibliografia
- [1] S.K. Berberian, The Weyl spectrum of an operator, Indiana Univ. Math. J. 20 (1970/1971), 529-544.
- [2] F.F. Bonsall, J. Duncan, Numerical ranges of operators on Normed spaces and of elements of normed algebras, London Mathematical Society Lecture Note Series, No. 2, Cambridge University Press, London-New York, 1971.
- [3] F.F. Bonsall, J. Duncan, Numerical ranges II, London Mathematical Society Lecture Notes Series, No. 10, Cambridge University Press, New York-London, 1973.
- [4] R.G. Douglas, Banach algebra techniques in operator theory, Academic Press, 1972. [5] K.E. Gustafson, D.K.M. Rao, Numerical Range, Springer-Verlag, New York, 1997. [6] P.R. Halmos, A Hilbert space problem book, Springer-Verlag, New-York, 1982.
- [7] S. Hildebrandt, fiber den Numerischen We.rtebere.ich eines Operators, Math. Ann. 163 (1966), 230-247.
- [8] G.J. Murphy, T.T. West, Spectral radius formulae, Proc. Edinburgh Math. Soc. 22 (1979), 271-275.
- [9] J.G. Stampfli, J.P. Williams, Growth conditions and the numerical range in a Banach algebra, Tohoku Math. Journ. 20 (1968), 417-424.
Typ dokumentu
Bibliografia
Identyfikator YADDA
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