Abstract
AbstractThe 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.
Publisher
Cambridge University Press (CUP)
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