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An algebraic derivative associated to the operator D δ

V. Almeida;  N. Castro;  J. Rodríguez — 2000

Banach Center Publications

In this paper we get an algebraic derivative relative to the convolution ( f * g ) ( t ) = ∫ 0 t i f ( t - ψ ) g ( ψ ) d ψ associated to the operator D δ , which is used, together with the corresponding operational calculus, to solve an integral-differential equation. Moreover we show a certain convolution property for the solution of that equation

Single valued extension property and generalized Weyl’s theorem

M. Berkani;  N. Castro;  S. V. Djordjević — 2006

Mathematica Bohemica

Let T be an operator acting on a Banach space X , let σ ( T ) and σ B W ( T ) be respectively the spectrum and the B-Weyl spectrum of T . We say that T satisfies the generalized Weyl’s theorem if σ B W ( T ) = σ ( T ) ∖ E ( T ) , where E ( T ) is the set of all isolated eigenvalues of T . The first goal of this paper is to show that if T is an operator of topological uniform descent and 0 is an accumulation point of the point spectrum of T , then T does not have the single valued extension property at 0 , extending an earlier result of J. K. Finch and a...

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