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1

Backward Aluthge iterates of a hyponormal operator and scalar extensions

100%

Benhida C., Zerouali E.

Studia Mathematica

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2009

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tom 195

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nr 1

1-10

EN

Let R and S be two operators on a Hilbert space. We discuss the link between the subscalarity of RS and SR. As an application, we show that backward Aluthge iterates of hyponormal operators and p-quasihyponormal operators are subscalar.

2

Back to RS-SR spectral theory

100%

Benhida C., Zerouali E.

Banach Center Publications

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2007

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tom 75

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nr 1

55-66

EN

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.

3

Bounded point evaluations for multicyclic operators

81%

EL Guendafi M., Mbekhta M., Zerouali E.

Banach Center Publications

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2005

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tom 67

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nr 1

199-217

EN

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 $ℬ_a = ℬ ∖ σ_{ap}(T)$. We introduce the concept of analytic structures and we link it to different spectral quantities. We apply this concept to retrieve in an easy way a theorem of D. Herrero and L. Rodman: the set of cyclic n-tuples for a multicyclic operator T is dense if and only if $ℬ_a = ∅$.

Ograniczanie wyników

2 Banach Center Publications

1 Studia Mathematica

3 Zerouali E.

2 Benhida C.

1 EL Guendafi M.

1 Mbekhta M.

1 2009

1 2007

1 2005

Backward Aluthge iterates of a hyponormal operator and scalar extensions

Back to RS-SR spectral theory

Bounded point evaluations for multicyclic operators