Hostname: page-component-7c8c6479df-ph5wq Total loading time: 0 Render date: 2024-03-28T08:24:29.676Z Has data issue: false hasContentIssue false

On the spectrum of C1 as an operator on bv0

Published online by Cambridge University Press:  09 April 2009

J. I. Okutoyi
Affiliation:
Kenyatta UniversityP.O. Box 43844 Nairobi, Kenya
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In 1985 John Reade determined the spectrum of C1 regarded as an operator on the space c0 of all null sequences normed by ║x║ = supn≧0|xn|. It is the purpose of this paper to determine the spectrum of C1 regarded as an operator on the space bv0 of all sequences x such that xk → 0 as k → ∞ and .

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1990

References

[1]Borwein, D., ‘On strong and absolute summability’, Proc. Glasgow Math. Assoc. 4 (1959), 8183.CrossRefGoogle Scholar
[2]Dunford, N. and Schwartz, J. T., Linear operators, Part I, General theory (John Wiley and Sons, 1967).Google Scholar
[3]Goldberg, S., Unbounded Linear operators-theory and applications, (McGraw-Hill, 1966).Google Scholar
[4]Hardy, G. H., Divergent series, (Oxford, 1949).Google Scholar
[5]Jakimovski, A. and Ramanujan, S. M., ‘A uniform approximation theorem and its application to moment problems’, Math. Z. 84 (1964), 143153.CrossRefGoogle Scholar
[6]Jakimovski, A. and Russel, D. C., ‘Matrix mappings between BK-spaces’, Bull. London Math. Soc. 4 (1972), 345353.CrossRefGoogle Scholar
[7]Kreysig, E., Introductory functional analysis with applications, (John Wiley and Sons, 1980).Google Scholar
[8]Leibowitz, G., ‘The Cesàro operators and their generalizations: Examples in infinite dimensional linear analysis.’ Amer. Math. Monthly 80 (1973), 654661.Google Scholar
[9]Maddox, I. J., Elements of functional analysis, (Cambridge Univ. Press, 1970).Google Scholar
[10]Reade, J. B., ‘On the spectrum of the Cesèro operator,’ Bull. London Math. Soc. 17 (1985), 263267.CrossRefGoogle Scholar
[11]Rhoades, B. E., ‘Spectra of some Hausdrff operators,’ Acta Sci. Math. (Szeged) 32 (1971), 91100.Google Scholar
[12]Stieglitz, M. and Tietz, H., ‘Matrixtranformationen von Folgenräumen. Eine Ergebnisübersicht,’ Math Z. 154 (1977), 116.CrossRefGoogle Scholar
[13]Taylor, A. E. and Lay, D. C., Introduction to functional analysis (2nd ed., John Wiley and Sons, 1980).Google Scholar