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Back to RS-SR spectral theory

C. BenhidaE. H. Zerouali — 2007

Banach Center Publications

Let X, Y be Banach spaces, S: X → Y and R: Y → X be bounded operators. We investigate common spectral properties of RS and SR. We then apply the result obtained to extensions, Aluthge transforms and upper triangular operator matrices.

Bounded point evaluations for multicyclic operators

M. EL GuendafiM. MbekhtaE. H. Zerouali — 2005

Banach Center Publications

Let T be a multicyclic operator defined on some Banach space. Bounded point evaluations and analytic bounded point evaluations for T are defined to generalize the cyclic case. We extend some known results on cyclic operators to the more general setting of multicyclic operators on Banach spaces. In particular we show that if T satisfies Bishop’s property (β), then a = σ a p ( T ) . We introduce the concept of analytic structures and we link it to different spectral quantities. We apply this concept to retrieve...

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