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Paper's Title:

Some interesting properties of finite continuous CesÓro operators

Author(s):

Abdelouahab Mansour and Abderrazak Hechifa

Operator theory laboratory (LABTHOP),
Eloued University,
Algeria.
E-mail: amansour@math.univ-lyon1.fr

Mathematics Department,
Faculty of Science,
Badji Mokhtar University, -Annaba,
Algeria.
E-mail: 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 C1 on Lp([0,1]), where C1 is the CesÓro operator defined on the complex Banach spaces Lp([0 , 1])  for 1<p<∞ by the expression


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