On the convex hull generated by orbit of operators

Rezaei, Hamid

doi:10.1016/j.laa.2013.02.002

Cited by 18 publications

(37 citation statements)

References 12 publications

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“…We next apply the previous proposition to infinite diagonal operators where A is the set of all convex polynomials. This extends the finite dimensional matrix result given by Rezaei [23,Corollary 2.7] to infinite dimensional diagonal matrices. are distinct and for every k ≥ 1 we have that λ k < −1.…”

Section: Diagonal Operators and Adjoint Multiplication Operatorssupporting

confidence: 78%

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On convex-cyclic operators

Bermúdez

Bonilla

Feldman

2016

Journal of Mathematical Analysis and Applications

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Abstract. We give a Hahn-Banach Characterization for convex-cyclicity. We also obtain an example of a bounded linear operator S on a Banach space with σ p (S * ) = ∅ such that S is convex-cyclic, but S is not weakly hypercyclic and S 2 is not convex-cyclic. This solved two questions of Rezaei in [23] when σ p (S * ) = ∅. We also characterize the diagonalizable normal operators that are convex-cyclic and give a condition on the eigenvalues of an arbitrary operator for it to be convex-cyclic. We show that certain adjoint multiplication operators are convex-cyclic and show that some are convex-cyclic but no convex polynomial of the operator is hypercyclic. Also some adjoint multiplication operators are convex-cyclic but not 1-weakly hypercyclic.

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Section: Diagonal Operators and Adjoint Multiplication Operatorssupporting

confidence: 78%

“…In [23] Rezaei asks the following question: Question 1. [23,Question 5.4] Is every convex-cyclic operator acting on an infinite dimensional Banach space weakly hypercyclic?…”

Section: Introductionmentioning

confidence: 99%

On convex-cyclic operators

Bermúdez

Bonilla

Feldman

2016

Journal of Mathematical Analysis and Applications

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“…, , and 0 + 1 +⋅ ⋅ ⋅+ = 1. We will focus our attention on the notion of convex cyclicity introduced by Rezaei in [3]. An operator is said to be convex cyclic if there exists a vector ∈ such that the real convex hull of the orbit (denoted by co(Orb( , ))) co (Orb ( , )) = { ( ) : convex polynomial} (2) is dense in .…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

“…In [3] are characterized the convex-cyclic matrices in finite dimension, and the author develops the main properties in the infinite dimensional setting.…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Powers of Convex-Cyclic Operators

León-Saavedra

Rosa²

2014

Abstract and Applied Analysis

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“…We are interested in operators that are convex-cyclic (Bermúdez, Bonilla, Feldman [1], León-Saavedra and Romero de la Rosa [7], Rezaei [8]). An operator T on the space X is called convex-cyclic if there is a vector x ∈ X such that the convex hull of its orbit is dense in X.…”

Section: Introductionmentioning

confidence: 99%

Convex Stone-Weierstrass theorems and invariant convex sets

Feldman¹,

McGuire²

2019

Rocky Mountain J. Math.

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A convex-polynomial is a convex combination of the monomials {1, x, x 2 , . . .}. This paper establishes that the convex-polynomials on R are dense in L p (µ) and weak * dense in L ∞ (µ), precisely when µ([−1, ∞)) = 0.It is shown that the convex-polynomials are dense in C(K) precisely whenwhere K is a compact subset of the real line. Moreover, the closure of the convex-polynomials on [−1, b] are shown to be the functions that have a convex-power series representation.A continuous linear operator T on a locally convex space X is convex-cyclic if there is a vector x ∈ X such that the convex hull of the orbit of x is dense in X. The above results characterize which multiplication operators on various real Banach spaces are convex-cyclic. It is shown for certain multiplication operators that every closed invariant convex set is a closed invariant subspace.

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On the convex hull generated by orbit of operators

Cited by 18 publications

References 12 publications

On convex-cyclic operators

On convex-cyclic operators

Powers of Convex-Cyclic Operators

Convex Stone-Weierstrass theorems and invariant convex sets

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