


Paper's Title:
Some interesting properties of finite continuous Cesàro operators
Author(s):
Abdelouahab Mansour and Abderrazak Hechifa
Operator theory laboratory (LABTHOP),
Eloued University,
Algeria.
Email:
amansour@math.univlyon1.fr
Mathematics Department,
Faculty of Science,
Badji Mokhtar University, Annaba,
Algeria.
Email:
abderrazak02@gmail.com
Abstract:
A complex scalar λ is called an extended eigenvalue of a bounded linear operator T on a complex Banach space if there is a nonzero operator X such that TX = λ XT, the operator X is called extended eigenoperator of T corresponding to the extended eigenvalue λ.
In this paper we prove some properties of extended eigenvalue and extended eigenoperator for C_{1} on L^{p}([0,1]), where C_{1} is the Cesàro operator defined on the complex Banach spaces L^{p}([0 , 1]) for 1<p<∞ by the expression
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