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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.)

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
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6. Esterle, J., Rate of decrease of sequences of powers in commutative radical Banach algebras, Pacific J. Math., to appear.Google Scholar
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