## Abstract and Applied Analysis

### Powers of Convex-Cyclic Operators

#### Abstract

A bounded operator $T$ on a Banach space $X$ is convex cyclic if there exists a vector $x$ such that the convex hull generated by the orbit ${\{{T}^{n}x\}}_{n\ge 0}$ is dense in $X$. In this note we study some questions concerned with convex-cyclic operators. We provide an example of a convex-cyclic operator $T$ such that the power ${T}^{n}$ fails to be convex cyclic. Using this result we solve three questions posed by Rezaei (2013).

#### Article information

Source
Abstr. Appl. Anal., Volume 2014, Special Issue (2014), Article ID 631894, 3 pages.

Dates
First available in Project Euclid: 2 October 2014

https://projecteuclid.org/euclid.aaa/1412278778

Digital Object Identifier
doi:10.1155/2014/631894

Mathematical Reviews number (MathSciNet)
MR3208553

Zentralblatt MATH identifier
07022782

#### Citation

León-Saavedra, Fernando; Romero-de la Rosa, María del Pilar. Powers of Convex-Cyclic Operators. Abstr. Appl. Anal. 2014, Special Issue (2014), Article ID 631894, 3 pages. doi:10.1155/2014/631894. https://projecteuclid.org/euclid.aaa/1412278778

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