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Supercyclicity of Convex Operators

Lotfollah Karimi|Karim Hedayatian
경북대학교 자연과학대학 수학과|2018.03|Kyungpook Mathematical Journal|제58권 제1호|pp. 81-90|DOI https://doi.org/10.5666/KMJ.2018.58.1.81

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키워드

supercyclicityhypercyclicityconvex operators
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초록

A bounded linear operator T on a Hilbert space H is convex, if for each $x \in \mathcal{H},$$\|T^{2}x\|^2-2\|Tx\|^2+\|x\|^2 \geq 0$. In this paper, it is shown that if T is convexand supercyclic then it is a contraction or an expansion. We then present some examplesof convex supercyclic operators. Also, it is proved that no convex composition operatorinduced by an automorphism of the disc on a weighted Hardy space is supercyclic.

Abstract

A bounded linear operator T on a Hilbert space H is convex, if for each $x \in \mathcal{H},$$\|T^{2}x\|^2-2\|Tx\|^2+\|x\|^2 \geq 0$. In this paper, it is shown that if T is convexand supercyclic then it is a contraction or an expansion. We then present some examplesof convex supercyclic operators. Also, it is proved that no convex composition operatorinduced by an automorphism of the disc on a weighted Hardy space is supercyclic.

참고문헌 (24)

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