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The Spectrum of Weighted Mean Operators

Published online by Cambridge University Press:  20 November 2018

B. E. Rhoades
B. E. Rhoades*
Affiliation:
Department of Mathematics Indiana University Bloomington, IN 47405 USA
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Abstract

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Recently J. B. Reade determined the spectrum of C, the Cesaro matrix of order 1, considered as an operator on cO, the space of null sequences. Previously F. P. A. Cass and the author had determined the spectra for a large class of weighted mean operators on c, the space of convergent sequences. Subsequently the author determined the fine spectra of these operators over c. This paper examines the spectra and fine spectra of weighted mean operators on cO, obtaining the result of Reade as a special case.

Keywords

40G9947A10
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 30 , Issue 4 , 01 December 1987 , pp. 446 - 449
Copyright
Copyright © Canadian Mathematical Society 1987

References

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4. Reade, J.B., On the spectrum of the Cesaro operator. Bull. London Math. Soc. 17 (1985), pp. 263–267.Google Scholar
5. Rhoades, B.E., The fine spectra for weighted mean operators. Pacific J. Math. 104 (1983), pp. 219–230.Google Scholar