Abstract and Applied Analysis

Powers of Convex-Cyclic Operators

Fernando León-Saavedra and María del Pilar Romero-de la Rosa

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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 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

Permanent link to this document
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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