RT Journal Article
T1 Orbits of Cesaro type operators
A1 León Saavedra, F.
A1 Piqueras Lerena, A.
A1 Seoane Sepúlveda, Juan Benigno
AB A bounded linear operator T on a Banach space X is called hypercyclic if there exists a vector x is an element of X such that its orbit, {T(n)x}, is dense in X. In this paper we show hypercyclic properties of the orbits of the Cesaro operator defined on different spaces. For instance, we show that the Cesaro operator defined on L(p)[0, 1] (1 < p < infinity) is hypercyclic. Moreover, it is chaotic and it has supercyclic subspaces. On the other hand, the Cesaro operator defined on other spaces of functions behave differently. Motivated by this, we study weighted Cesaro operators and different degrees of hypercyclicity are obtained. The proofs are based on the classical Muntz-Szasz theorem. We also propose problems and give new directions.
PB Wiley-Blackwell
SN 0025-584X
YR 2009
FD 2009
LK https://hdl.handle.net/20.500.14352/50458
UL https://hdl.handle.net/20.500.14352/50458
LA eng
NO Junta de Andalucia
NO UCA
NO Junta de Andalucıa
DS Docta Complutense
RD 9 abr 2025