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SUPERCYCLIC SUBSPACES

Published online by Cambridge University Press:  08 October 2003

ALFONSO MONTES-RODRÍGUEZ
Affiliation:
Departamento de Análisis Matemático, Facultad de Matemáticas, Avenida Reina Mercedes, Apartado 1160 Sevilla 41080, Spain, amontes@us.es
HÉCTOR N. SALAS
Affiliation:
Departamento de Matemáticas, Universidad de Puerto Rico, Mayagüez, Puerto Rico 00681, salas@math.uprm.edu
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Abstract

A bounded operator $T$ acting on a Banach space $\cal B$ is said to be supercyclic if there is a vector $x\,{\in}\,\cal B$ such that the projective orbit $\{\lambda T^n x\,{:}\,n\,{\geq}\,0\text{ and } \lambda\,{\in}\,\Bbb C \}$ is dense in $\cal B$. Examples of supercyclic operators are hypercyclic operators, in which the orbit itself is dense without the help of scalar multiples. Supercyclic operators are, in turn, a special case of cyclic operators. An operator is called cyclic if the linear span of the orbit of some vector is dense in the underlying space. This survey describes some recent results on linear subspaces in which all elements, except the zero vector, are supercyclic for a given supercyclic operator.

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Notes and Papers
Copyright
© The London Mathematical Society 2003

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