Asymptotic behavior of polynomially bounded operators

Mustafayev, Heybetkulu

doi:10.1016/j.crma.2010.04.003

Cited by 9 publications

(4 citation statements)

References 5 publications

(4 reference statements)

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“…This result has in turn been improved upon in two recent papers. In [20], Léka has extended this result to power-bounded operators on Hilbert space, and Zarrabi in [30] has shown that for contractions, and likewise for pairs of commuting contractions and for contractive C 0 -semigroups, the limit appearing in (1.1) is given, more generally, by sup{| a(λ)| : λ ∈ σ(T ) ∩ T} or the appropriate analogue; for related results see [2], [3], [9], [10] and [22]. The purpose of this paper is to improve both Léka's and Zarrabi's versions of the Katznelson-Tzafriri theorem by extending them to representations of a significantly larger class of semigroups.…”

Section: Introductionmentioning

confidence: 99%

Some improvements of the Katznelson- Tzafriri theorem on Hilbert space

Seifert¹

2015

Proc. Amer. Math. Soc.

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Abstract. This paper extends two recent improvements in the Hilbert space setting of the well-known Katznelson-Tzafriri theorem by establishing both a version of the result valid for bounded representations of a large class of abelian semigroups and a quantified version for contractive representations. The paper concludes with an outline of an improved version of the KatznelsonTzafriri theorem for individual orbits, whose validity extends even to certain unbounded representations.

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Section: Introductionmentioning

confidence: 99%

Some improvements of the Katznelson- Tzafriri theorem on Hilbert space

Seifert¹

2015

Proc. Amer. Math. Soc.

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“…Notice that result (b) was obtained simultaneously in [7,8] (the present paper is an improved version of [7]). For the proof of (a) and (b) we use in particular the von Neumann inequality ( [9]), while a different method is used for (c).…”

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confidence: 57%

Some results of Katznelson–Tzafriri type

Zarrabi¹

2013

Journal of Mathematical Analysis and Applications

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a b s t r a c tFor semigroups S = R + , Z + and Z kof a suitable semigroup S by contractions on a Banach space, we give sharp conditions on Sp u (T , S) which guarantee that the equality above holds. These conditions concern the thinness of Sp u (T , S) in the harmonic analysis sense. These results are related to theorems of Katznelson-Tzafriri type, which give conditions guaranteeing that inf t∈S ∥T (t)  f (T )∥ vanishes.

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“…In this paper, we address the problem whether local and quantitative versions of the Nagy-Foias Theorem hold. For related results see (Allan and Ransford, 1989;Batty et al, 1998;Mustafayev, 2010).…”

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confidence: 94%