Hildebrandt's theorem for the essential spectrum

• Autorzy: Bracic J. , Diogo C.

Identyfikatory

DOI

http://dx.doi.Org/10.7494/OpMath.2015.35.3.279

• Języki publikacji: EN

Abstrakty

EN

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

EN

essential spectrum; Hildebrandt's theorem; essential numerical range

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2015
• Tom: Vol. 35, no. 3
• Strony: 279--285
• Opis fizyczny: Bibliogr. 9 poz.

Twórcy

autor

Bracic J.

• University ol Ljubljana, IMFM Jadranska ul. 19 SI-1000 Ljubljana Slovenia

autor

Diogo C.

• Instituto Universitario de Lisboa Departamento de Matematica Av. das Forcas

Bibliografia

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• [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.