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Local spectrum and Kaplansky's theorem on algebraic operators

100%

Drissi D.

Colloquium Mathematicum

1998

tom 75

nr 2

159-165

Using elementary arguments we improve former results of P. Vrbová concerning local spectrum. As a consequence, we obtain a new proof of Kaplansky’s theorem on algebraic operators on a Banach space.

On a theorem of Gelfand and its local generalizations

100%

Drissi D.

Studia Mathematica

1997

tom 123

nr 2

185-194

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.

Ograniczanie wyników

1 Colloquium Mathematicum

1 Studia Mathematica

2 Drissi D.

1 1998

1 1997

Wyniki wyszukiwania

Local spectrum and Kaplansky's theorem on algebraic operators

On a theorem of Gelfand and its local generalizations