On Ergodic Operator Means in Banach Spaces

Aleman, Alexandru; Suciu, Laurian

doi:10.1007/s00020-016-2298-x

Cited by 19 publications

(43 citation statements)

References 29 publications

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“…Hence, in this case, by Lemma 2.1, T b cannot be supercyclic. Now, we find an operator that is power bounded and not supercyclic on a Fréchet space; see [2,13,14] for different situations in Banach spaces. This example shows that for a power bounded operator, the thesis in Theorem 2.3 is not sufficient for the operator to be supercyclic.…”

Section: Examplesmentioning

confidence: 96%

A Note on Supercyclic Operators in Locally Convex Spaces

Albanese

Jornet

2019

Mediterr. J. Math.

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Section: Examplesmentioning

confidence: 96%

A Note on Supercyclic Operators in Locally Convex Spaces

Albanese

Jornet

2019

Mediterr. J. Math.

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“…In this section we present a method to construct a Hilbert space H k and an (m + 1)isometry on H k from an m-isometry T k on a Hilbert space for some integer k. Our result is based on the construction given by Aleman and Suciu in [7,Proposition 5.2] for m = 2 and k = 1.…”

Section: Construction Of An (M + 1)-isometry From An M-isometrymentioning

confidence: 99%

Some Examples of m-Isometries

2020

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We obtain the admissible sets on the unit circle to be the spectrum of a strict m-isometry on an n-finite dimensional Hilbert space. This property gives a better picture of the correct spectrum of an m-isometry. We determine that the only m-isometries on R 2 are 3-isometries and isometries giving by ±I + Q, where Q is a nilpotent operator. Moreover, on real Hilbert space, we obtain that m-isometries preserve volumes. Also we present a way to construct a strict (m + 1)-isometry with an m-isometry given, using ideas of Aleman and Suciu [7, Proposition 5.2] on infinite dimensional Hilbert space.Date: February 25, 2019.2010 Mathematics Subject Classification. 47A05. Key words and phrases. m-isometry, strict m-isometry, weighted shift operator, isometric n-Jordan operator, sub-isometric n-Jordan operator, finite dimensional space, k-volume.

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“…The Ansari-Bourdon theorem mentioned above about the non supercyclicity of isometries on Banach spaces is a consequence of a theorem which asserts that for a supercyclic power bounded operator T defined on a Banach space, the orbits of the adjoint T * are everywhere ω * convergent to 0. For recent research extending these classic results we refer to [1,2,13]. In the last section of the paper we use our results about weighted composition operators to get results for arbitrary operators defined on locally convex spaces, obtaining conditions in the dynamics of the adjoint T ′ which are necessary for T being weakly supercyclic.…”

Section: Introductionmentioning

confidence: 99%

Supercyclicity of weighted composition operators on spaces of continuous functions

2019

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Our study is focused on the dynamics of weighted composition operators defined on a locally convex space E ֒→ (C(X), τ p ) with X being a topological Hausdorff space containing at least two different points and such that the evaluations {δ x : x ∈ X} are linearly independent in E ′ . We prove, when X is compact and E is a Banach space containing a nowhere vanishing function, that a weighted composition operator C w,ϕ is never weakly supercyclic on E. We also prove that if the symbol ϕ lies in the unit ball of A(D), then every weighted composition operator can never be τ psupercyclic neither on C(D) nor on the disc algebra A(D). Finally, we obtain Ansari-Bourdon type results and conditions on the spectrum for arbitrary weakly supercyclic operators, and we provide necessary conditions for a composition operator to be weakly supercyclic on the space of holomorphic functions defined in non necessarily simply connected planar domains. As a consequence, we show that no composition operator can be weakly supercyclic neither on the space of holomorphic functions on the punctured disc nor in the punctured plane.

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On Ergodic Operator Means in Banach Spaces

Cited by 19 publications

References 29 publications

A Note on Supercyclic Operators in Locally Convex Spaces

A Note on Supercyclic Operators in Locally Convex Spaces

Some Examples of m-Isometries

Supercyclicity of weighted composition operators on spaces of continuous functions

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