Geodesic
THE CESÀRO OPERATOR IN THE FRÉCHET SPACES lp+ AND L p−
Glasgow mathematical journal, Tome 59 (2017) no. 2, pp. 273-287

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DOI

The classical spaces lp+, 1 ≤ p < ∞, and L p−, 1<p ≤ ∞, are countably normed, reflexive Fréchet spaces in which the Cesàro operator C acts continuously. A detailed investigation is made of various operator theoretic properties of C (e.g., spectrum, point spectrum, mean ergodicity) as well as certain aspects concerning the dynamics of C (e.g., hypercyclic, supercyclic, chaos). This complements the results of [3, 4], where C was studied in the spaces CN, L p loc(R+) for 1 < p < ∞ and C(R+), which belong to a very different collection of Fréchet spaces, called quojections; these are automatically Banach spaces whenever they admit a continuous norm. 
ALBANESE, ANGELA A.; BONET, JOSÉ; RICKER, WERNER J. THE CESÀRO OPERATOR IN THE FRÉCHET SPACES lp+ AND L p−. Glasgow mathematical journal, Tome 59 (2017) no. 2, pp. 273-287. doi: 10.1017/S001708951600015X
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     title = {THE {CES\`ARO} {OPERATOR} {IN} {THE} {FR\'ECHET} {SPACES} lp+ {AND} {L} p\ensuremath{-}},
     journal = {Glasgow mathematical journal},
     pages = {273--287},
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     doi = {10.1017/S001708951600015X},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S001708951600015X/}
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