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1997 | 123 | 2 | 185-194
Tytuł artykułu

On a theorem of Gelfand and its local generalizations

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Abstrakty
EN
In 1941, I. Gelfand proved that if a is a doubly power-bounded element of a Banach algebra A such that Sp(a) = {1}, then a = 1. In [4], this result has been extended locally to a larger class of operators. In this note, we first give some quantitative local extensions of Gelfand-Hille's results. Secondly, using the Bernstein inequality for multivariable functions, we give short and elementary proofs of two extensions of Gelfand's theorem for m commuting bounded operators, $T_1,..., T_m$, on a Banach space X.
Twórcy
autor
  • Department of Mathematics and Computer Science, Faculty of Science, Kuwait University, P.O. Box 5969 Safat 13060, Kuwait, drissi@math-1.sci.kuniv.edu.kw
Bibliografia
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