Journal of Operator Theory

Volume 79, Issue 2, Spring 2018 pp. 373-402.

The Cesaro operator on duals of power series spaces of infinite type

Authors: Angela A. Albanese (1) Jose Bonet (2) and Werner J. Ricker (3)
Author institution: (1) Dipartimento di Matematica e Fisica ``E. De Giorgi'', Universita del Salento- C.P.193, I-73100 Lecce, Italy
(2) Instituto Universitario de Matematica Pura y Aplicada IUMPA, Universitat Politecnica de Valencia, E-46071 Valencia, Spain
(3) Mathematisch-Geographische Fakultaet, Katholische Universitaet Eichstaett-Ingolstadt, D-85072 Eichstatt, Germany

Summary: A detailed investigation is made of the continuity, spectrum and mean ergodic properties of the Ces\`aro operator $\mathsf{C}$ when acting on the strong duals of power series spaces of infinite type. There is a dramatic difference in the nature of the spectrum of $\mathsf{C}$ depending on whether or not the strong dual space (which is always Schwartz) is nuclear.

DOI: http://dx.doi.org/10.7900/jot.2017apr20.2173
Keywords: Ces\`aro operator, duals of power series spaces, spectrum, (LB)-space, mean ergodic operator, nuclear space

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