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Power-bounded elements and tauberian theorems in locally convex algebras

Published online by Cambridge University Press:  24 October 2008

M. A. Hennings
M. A. Hennings
Affiliation:
Sidney Sussex College, Cambridge, CB2 3HU
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Abstract

The tauberian theorems concerning power-bounded elements of Banach algebras studied by Katznelson and Tzafriri, Allan, O'Farrell and Ransford and Allan are considered, and it is shown that (almost) exactly the same results are true for power-bounded elements in a very large class of locally convex topological algebras, the pseudo-complete algebras. The submultiplicativity of the Banach algebra norm is, for once, inessential to the proof of these theorems.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 105 , Issue 1 , January 1989 , pp. 147 - 159
Copyright
Copyright © Cambridge Philosophical Society 1989

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References

REFERENCES

[1]Allan, G. R.. A spectral theory for locally convex algebras. Proc. London Math. Soc. (3) 15 (1965), 399–421.CrossRefGoogle Scholar
[2]Allan, G. R.. Power-bounded elements and a theorem of Gel'fand. (Preprint, 1987.)Google Scholar
[3]Allan, G. R., O'Farrell, A. G. and Ransfoed, T. J.. A tauberian theorem arising in operator theory. (Preprint, 1986.)Google Scholar
[4]Bachelis, G. F. and Saeki, S.. Power-bounded elements in a Banach algebra with small peripheral spectrum. (Preprint, 1986.)Google Scholar
[5]Crabb, M. J. and Duncan, J.. Some inequalities for norm unitaries in Banach algebras. Proc. Edinburgh Math. Soc. (2) 21 (1978), 17–23.CrossRefGoogle Scholar
[6]Fand, I. M. Gel'. Zur Theorie der Charaktere der abelschen topologischen Gruppen. Mat. Sb. (N.S.) 9 (1941), 49–50.Google Scholar
[7]Husain, T.. Multiplicative Functionals on Topological Algebras. Research Notes in Math. no. 85 (Pitman, 1983).Google Scholar
[8]Husain, T. and Warsi, S. A.. Positive functionals on BP*-algebras. Period. Math. Hung. 8 (1977), 15–28.CrossRefGoogle Scholar
[9]Katznelson, Y. and Tzafriri, L.. On power-bounded operators. J. Funct. Anal. 68 (1986), 313–328.CrossRefGoogle Scholar
[10]Mallios, A.. Topological Algebras, Selected Topics North-Holland Math. Studies no. 124 (North-Holland, 1986).Google Scholar