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On the continuous Cesàro operator in certain function spaces

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On the continuous Cesàro operator in certain function spaces

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Albanese, AA.; Bonet Solves, JA.; Ricker, WJ. (2015). On the continuous Cesàro operator in certain function spaces. Positivity. 19:659-679. doi:10.1007/s11117-014-0321-5

Por favor, use este identificador para citar o enlazar este ítem: http://hdl.handle.net/10251/71238

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Title: On the continuous Cesàro operator in certain function spaces
Author: Albanese, Angela A. Bonet Solves, José Antonio Ricker, Werner Joseph
UPV Unit: Universitat Politècnica de València. Escuela Técnica Superior de Arquitectura - Escola Tècnica Superior d'Arquitectura
Universitat Politècnica de València. Instituto Universitario de Matemática Pura y Aplicada - Institut Universitari de Matemàtica Pura i Aplicada
Issued date:
Abstract:
Various properties of the (continuous) Cesàro operator C, acting on Banach and Fréchet spaces of continuous functions and L p-spaces, are investigated. For instance, the spectrum and point spectrum of C are completely ...[+]
Subjects: Cesàro operator , Continuous function spaces , Lp-spaces , (Uniformly) mean ergodic operator , Hypercyclic operator , Supercyclic operator
Copyrigths: Reserva de todos los derechos
Source:
Positivity. (issn: 1385-1292 )
DOI: 10.1007/s11117-014-0321-5
Publisher:
Springer Verlag (Germany)
Publisher version: http://dx.doi.org/10.1007/s11117-014-0321-5
Description: “The final publication is available at Springer via http://dx.doi.org/10.1007/s11117-014-0321-5"
Thanks:
The research of the first two authors was partially supported by the projects MTM2010-15200 and GVA Prometeo II/2013/013 (Spain). The second author gratefully acknowledges the support of the Alexander von Humboldt Foundation.[+]
Type: Artículo

References

Albanese, A.A.: Primary products of Banach spaces. Arch. Math. 66, 397–405 (1996)

Albanese, A.A.: On subspaces of the spaces $$L^p_{\rm loc}$$ L loc p and of their strong duals. Math. Nachr. 197, 5–18 (1999)

Albanese, A.A., Moscatelli, V.B.: Complemented subspaces of sums and products of copies of $$L^1 [0,1]$$ L 1 [ 0 , 1 ] . Rev. Mat. Univ. Complut. Madr. 9, 275–287 (1996) [+]
Albanese, A.A.: Primary products of Banach spaces. Arch. Math. 66, 397–405 (1996)

Albanese, A.A.: On subspaces of the spaces $$L^p_{\rm loc}$$ L loc p and of their strong duals. Math. Nachr. 197, 5–18 (1999)

Albanese, A.A., Moscatelli, V.B.: Complemented subspaces of sums and products of copies of $$L^1 [0,1]$$ L 1 [ 0 , 1 ] . Rev. Mat. Univ. Complut. Madr. 9, 275–287 (1996)

Albanese, A.A., Bonet, J., Ricker, W.J.: Mean ergodic operators in Fréchet spaces. Ann. Acad. Sci. Fenn. Math. 34, 401–436 (2009)

Albanese, A.A., Bonet, J., Ricker, W.J.: On mean ergodic operators. In: Curbera, G.P. (eds.) Vector Measures, Integration and Related Topics. Operator Theory: Advances and Applications, vol. 201, pp. 1–20. Birkhäuser, Basel (2010)

Albanese, A.A., Bonet, J., Ricker, W.J.: $$C_0$$ C 0 -semigroups and mean ergodic operators in a class of Fréchet spaces. J. Math. Anal. Appl. 365, 142–157 (2010)

Albanese, A.A., Bonet, J., Ricker, W.J.: Convergence of arithmetic means of operators in Fréchet spaces. J. Math. Anal. Appl. 401, 160–173 (2013)

Bayart, F., Matheron, E.: Dynamics of linear operators. Cambridge Tracts in Mathematics, vol. 179. Cambridge University Press, Cambridge (2009)

Bellenot, S.F., Dubinsky, E.: Fréchet spaces with nuclear Köthe quotients. Trans. Am. Math. Soc. 273, 579–594 (1982)

Bonet, J., Frerick, L., Peris, A., Wengenroth, J.: Transitive and hypercyclic operators on locally convex spaces. Bull. Lond. Math. Soc. 37, 254–264 (2005)

Boyd, D.W.: The spectrum of the Cesàro operator. Acta Sci. Math. (Szeged) 29, 31–34 (1968)

Brown, A., Halmos, P.R., Shields, A.L.: Cesàro operators. Acta Sci. Math. (Szeged) 26, 125–137 (1965)

Dierolf, S., Zarnadze, D.N.: A note on strictly regular Fréchet spaces. Arch. Math. 42, 549–556 (1984)

Dunford, N., Schwartz, J.T.: Linear Operators I: General Theory (2nd Printing). Wiley-Interscience, New York (1964)

Galaz Fontes, F., Solís, F.J.: Iterating the Cesàro operators. Proc. Am. Math. Soc. 136, 2147–2153 (2008)

Galaz Fontes, F., Ruiz-Aguilar, R.W.: Grados de ciclicidad de los operadores de Cesàro–Hardy. Misc. Mat. 57, 103–117 (2013)

González, M., León-Saavedra, F.: Cyclic behaviour of the Cesàro operator on $$L_2(0,+\infty )$$ L 2 ( 0 , + ∞ ) . Proc. Am. Math. Soc. 137, 2049–2055 (2009)

Grosse-Erdmann, K.G., Peris Manguillot, A.: Linear chaos. In: Universitext. Springer, London (2011)

Hardy, G.H., Littlewood, J.E., Pólya, G.: Inequalities. In: Reprint of the 1952 Edition. Cambridge Mathematical Library. Cambridge University Press, Cambridge (1988)

Krengel, U.: Ergodic theorems. In: De Gruyter Studies in Mathematics, vol. 6. Walter de Gruyter Co., Berlin (1985)

Leibowitz, G.M.: Spectra of finite range Cesàro operators. Acta Sci. Math. (Szeged) 35, 27–28 (1973)

Leibowitz, G.M.: The Cesàro operators and their generalizations: examples in infinite-dimensional linear analysis. Am. Math. Mon. 80, 654–661 (1973)

León-Saavedra, F., Piqueras-Lerena, A., Seoane-Sepúlveda, J.B.: Orbits of Cesàro type operators. Math. Nachr. 282, 764–773 (2009)

Lin, M.: On the uniform ergodic theorem. Proc. Am. Math. Soc. 43, 337–340 (1974)

Meise, R., Vogt, D.: Introduction to functional analysis. In: Oxford Graduate Texts in Mathematics, vol. 2. The Clarendon Press; Oxford University Press, New York (1997)

Metafune, G., Moscatelli, V.B.: Quojections and prequojections. In: Terzioğlu, T. (ed.) Advances in the Theory of Fréchet spaces. NATO ASI Series, vol. 287, pp. 235–254. Kluwer Academic Publishers, Dordrecht (1989)

Moscatelli, V.B.: Fréchet spaces without norms and without bases. Bull. Lond. Math. Soc. 12, 63–66 (1980)

Piszczek, K.: Quasi-reflexive Fréchet spaces and mean ergodicity. J. Math. Anal. Appl. 361, 224–233 (2010)

Piszczek, K.: Barrelled spaces and mean ergodicity. Rev R. Acad. Cienc. Exactas Fis. Nat. Ser. A Math. RACSAM 104, 5–11 (2010)

Yosida, K.: Functional Analysis, 6th edn. Springer, Berlin (1980)

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