TY - JOUR
AU - Bermúdez, T.
AU - Bonilla, A.
AU - Feldman, N.S.
T1 - On convex-cyclic operators
LA - eng
PY - 2016
SP - 1166
EP - 1181
T2 - Journal of Mathematical Analysis and Applications
SN - 1096-0813
VL - 434
IS - 2
PB - Academic Press Inc.
AB - We give a Hahn-Banach characterization for convex-cyclicity. We also obtain an example of a bounded linear operator S on a Banach space with σp(S*)=θ such that S is convex-cyclic, but S is not weakly hypercyclic and S2 is not convex-cyclic. This solved two questions of Rezaei in [25] when σp(S*)=θ. We also characterize the diagonalizable normal operators that are convex-cyclic and give a condition on the eigenvalues of an arbitrary operator for it to be convex-cyclic. We show that certain adjoint multiplication operators are convex-cyclic and show that some are convex-cyclic but no convex polynomial of the operator is hypercyclic. Also some adjoint multiplication operators are convex-cyclic but not 1-weakly hypercyclic.
DO - 10.1016/J.JMAA.2015.09.053
UR - https://portalciencia.ull.es/documentos/5e3c3c5329995246bbf606d0
DP - Dialnet - Portal de la Investigación
ER -