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Irregularity of the Rate of Decrease of Sequences of Powers in the Volterra Algebra

Published online by Cambridge University Press:  20 November 2018

J. Esterle
J. Esterle*
Affiliation:
UCLA, Los Angeles, California
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G. R. Allan and A. M. Sinclair proved in [1] that if a commutative radical Banach algebra possesses bounded approximate identities then for every sequence (αn ) of real numbers such that limn→∞ αn = 0 there exists such that

In the other direction it is shown in [6] that if is separable and if the nilpotents are dense in then for every sequence (βn ) of positive reals there exists such that

(This result was given in [2] for the Volterra algebra.)

Information

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 33 , Issue 2 , 01 April 1981, pp. 320 - 324
Copyright
Copyright © Canadian Mathematical Society 1981

References

1. Allan, G. R. and Sinclair, A. M., Power factorization in Banach algebras with bounded approximate identity, Studia Math. 56 (1976), 31–38.Google Scholar
2. Bade, W. G. and Dales, H. G., Norms and ideals in some radical Banach algebra s, preprint.Google Scholar
3. Cohen, P. J., Factorization in group algebras, Duke Math. J. 26 (1959), 199–206.Google Scholar
4. Dales, H. G., Automatic continuity, a survey, Bull. London Math. Soc. 10 (1978), 129–183.Google Scholar
5. Esterle, J., Theorems of Gelfand Mazur type and continuity of epimorphisms from , J. Functional Analysis, to appear.Google Scholar
6. Esterle, J., Rate of decrease of sequences of powers in commutative radical Banach algebras, Pacific J. Math., to appear.Google Scholar
7. Johnson, B. E., Continuity of centralizers on Banach algebras, J. London Math. Soc. J+l (1966), 639–640.Google Scholar
8. Varopoulos, N., Continuité des formes linéaires positives sur une algèbre de Banach avec involution, C.R. Acad., Sci. Paris Ser. A258 (1964), 1121.Google Scholar