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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
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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.)
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- Copyright © Canadian Mathematical Society 1981
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