Powers of Convex-Cyclic Operators

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...

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Bibliographic Details
Published inAbstract and Applied Analysis Vol. 2014; no. 2014; pp. 472 - 474-1046
Main Authors Fernando León-Saavedra, María del Pilar Romero-de la Rosa
Format Journal Article
LanguageEnglish
Published Cairo, Egypt Hindawi Limiteds 01.01.2014
Hindawi Publishing Corporation
Hindawi Limited
Wiley
Subjects
Convex functions
Mathematical research
Operator theory
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Summary: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).
ISSN:1085-3375
1687-0409
DOI:10.1155/2014/631894