Powers of Convex‐Cyclic Operators

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

Abstract and Applied Analysis, 2014, vol. 2014, issue 1

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 Tnxn≥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 Tn fails to be convex cyclic. Using this result we solve three questions posed by Rezaei (2013).

Date: 2014
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https://doi.org/10.1155/2014/631894

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:631894

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