Local spectrum and Kaplansky's theorem on algebraic operators

• Autorzy: Driss Drissi
• Języki publikacji: EN

Abstrakty

EN

Using elementary arguments we improve former results of P. Vrbová concerning local spectrum. As a consequence, we obtain a new proof of Kaplansky’s theorem on algebraic operators on a Banach space.

Słowa kluczowe

EN

local spectral radius; local spectrum; algebraic operators

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 1998
• Tom: 75
• Numer: 2
• Strony: 159-165

Daty

wydano

1998

otrzymano

1997-01-27

Twórcy

autor

Driss Drissi

• Department of Mathematics and Computer Science, Faculty of Science, Kuwait University, P.O. Box 5969, Safat 13060, Kuwait

Bibliografia

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• [2] B. Aupetit and D. Drissi, Local spectrum and subharmonicity, Proc. Edinburgh Math. Soc. 39 (1996), 571-579.
• [3] I. Colojoară and C. Foiaş, Theory of Generalized Spectral Operators, Gordon and Breach, 1968.
• [4] N. Dunford, A survey of the theory of spectral operators, Bull. Amer. Math. Soc. 64 (1958), 217-274.
• [5] I. Erdelyi and R. Lange, Spectral Decompositions on Banach Spaces, Lecture Notes in Math. 623, Springer, 1977.
• [6] C. Foiaş and F.-H. Vasilescu, On the spectral theory of commutators, J. Math. Anal. Appl. 31 (1970), 473-486.
• [7] J. D. Gray, Local analytic extensions of the resolvent, Pacific J. Math. 27 (1968), 305-324.
• [8] P. R. Halmos, A Hilbert Space Problem Book, D. Van Nostrand, 1967.
• [9] I. Kaplansky, Infinite Abelian Groups, Univ. of Michigan Press, 1969.
• [10] P. Vrbová, On local spectral properties of operators in Banach spaces, Czechoslovak Math. J. 23 (1973), 483-492.