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The fine spectrum of the Cesàro operator in $$\ell _ p(1<p<\infty)$$. (English) Zbl 0568.47021
See the preview in Zbl 0548.47016.

##### MSC:
 47B37 Linear operators on special spaces (weighted shifts, operators on sequence spaces, etc.) 47A10 Spectrum, resolvent 46A45 Sequence spaces (including Köthe sequence spaces) 40G05 Cesàro, Euler, Nörlund and Hausdorff methods
##### Keywords:
fine spectrum of the Cesàro matrix; state diagrams
Zbl 0548.47016
Full Text:
##### References:
 [1] A.Bouvier, Théorie élémentaire des séries. Paris 1971. [2] A. Brown, P. R. Halmos andA. L. Shields, Cesàro operators. Acta Sci. Math.26, 125-137 (1965). · Zbl 0149.09902 [3] A. P. Calderón, Intermediate spaces and interpolation. The complex method. Studia Math.24, 113-190 (1964). · Zbl 0204.13703 [4] B. E. Rhoades, Spectra of some Hausdorff operators. Acta Sci. Math.32, 91-100 (1971). · Zbl 0223.47017 [5] B. E. Rhoades, Generalized Hausdorff matrices bounded onl p andc. Acta Sci. Math.43, 333-345 (1981). · Zbl 0487.40003 [6] B. E. Rhoades, The fine spectra for weighted mean operators. Pacific J. Math.104, 219-230 (1983). · Zbl 0501.40007 [7] A. E.Taylor and D. C.Lay, Introduction to functional analysis. New York 1980. · Zbl 0501.46003 [8] R. B. Wenger, The fine spectra of the Holder summability operators. Indian J. Pure Appl. Math.6, 695-712 (1975). · Zbl 0362.40010
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