I just received the news that my paper entitled Extended eigenvalues for Cesàro operators has been accepted for its publication in the Journal of Mathematical Analysis and Applications. This is joint work with Fernando León-Saavedra (Jerez de la Frontera), Srdjan Petrovic (Kalamazoo) and Omid Zabeti (Sistan and Baluchestan). Here is the abstract of the paper.
A complex scalar is said to be an extended eigenvalue of a bounded linear operator on a complex Banach space if there is a nonzero operator such that Such an operator is called an extended eigenoperator of corresponding to the extended eigenvalue
The purpose of this paper is to give a description of the extended eigenvalues for the discrete Cesàro operator the finite continuous Cesàro operator and the infinite continuous Cesàro operator defined on the complex Banach spaces and for by the expressions
It is shown that the set of extended eigenvalues for is the interval that for it is the interval and that for it reduces to the singleton