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• W2964261793 endingPage "657" @default.
• W2964261793 startingPage "623" @default.
• W2964261793 abstract "A complex scalar λ is said to be an extended eigenvalue of a bounded linear operator T on a complex Banach space if there is a non-zero operator X such that TX=λXT. Such an operator X is called an extended eigenoperator of T corresponding to the extended eigenvalue λ. The purpose of this paper is to give a description of the extended eigenvalues for the discrete Cesàro operator C0, the finite continuous Cesàro operator C1 and the infinite continuous Cesàro operator C∞ defined on the complex Banach spaces ℓp, Lp[0,1] and Lp[0,∞) for 1<p<∞ by the expressions(C0f)(n):=1n+1∑k=0nf(k),(C1f)(x):=1x∫0xf(t)dt,(C∞f)(x):=1x∫0xf(t)dt. It is shown that the set of extended eigenvalues for C0 is the interval [1,∞), for C1 it is the interval (0,1], and for C∞ it reduces to the singleton {1}." @default.
• W2964261793 created "2019-07-30" @default.
• W2964261793 creator A5019722092 @default.
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• W2964261793 creator A5091789856 @default.
• W2964261793 date "2015-09-01" @default.
• W2964261793 modified "2023-09-30" @default.
• W2964261793 title "Extended eigenvalues for Cesàro operators" @default.
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• W2964261793 doi "https://doi.org/10.1016/j.jmaa.2015.04.028" @default.
• W2964261793 hasPublicationYear "2015" @default.
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