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Cesaro bounded operators in Banach spaces

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Cesaro bounded operators in Banach spaces

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Bermúdez, T.; Bonilla, A.; Muller, V.; Peris Manguillot, A. (2020). Cesaro bounded operators in Banach spaces. Journal d Analyse Mathématique. 140(1):187-206. https://doi.org/10.1007/s11854-020-0085-8

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Título: Cesaro bounded operators in Banach spaces
Autor: Bermúdez, Teresa Bonilla, Antonio Muller, Vladimir Peris Manguillot, Alfredo
Entidad UPV: Universitat Politècnica de València. Departamento de Matemática Aplicada - Departament de Matemàtica Aplicada
Fecha difusión:
Resumen:
[EN] We study several notions of boundedness for operators. It is known that any power bounded operator is absolutely Cesaro bounded and strongly Kreiss bounded (in particular, uniformly Kreiss bounded). The converses do ...[+]
Palabras clave: Cesàro bounded operators , Kreiss bounded operators , Mean ergodic operators , Mixing
Derechos de uso: Reserva de todos los derechos
Fuente:
Journal d Analyse Mathématique. (issn: 0021-7670 )
DOI: 10.1007/s11854-020-0085-8
Editorial:
Springer-Verlag
Versión del editor: https://doi.org/10.1007/s11854-020-0085-8
Código del Proyecto:
info:eu-repo/grantAgreement/GACR//17-27844S/
info:eu-repo/grantAgreement/GACR//67985840/
info:eu-repo/grantAgreement/MINECO//MTM2016-75963-P/ES/DINAMICA DE OPERADORES/
info:eu-repo/grantAgreement/GVA//PROMETEO%2F2017%2F102/ES/ANALISIS FUNCIONAL, TEORIA DE OPERADORES Y APLICACIONES/
Agradecimientos:
The first, second and fourth authors were supported by MINECO and FEDER, Project MTM201675963-P. The third author was supported by grant No. 17-27844S of GA CR and RVO: 67985840. The fourth author was also supported by ...[+]
Tipo: Artículo

References

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

A. Aleman and L. Suciu, On ergodic operator means in Banach spaces, Integral Equations Operator Theory 85 (2016), 259–287.

I. Assani, Sur les opérateurs à puissances bornées et le théorème ergodique ponctuel dans Lp[0, 1], 1 < p < ∞, Canad. J. Math. 38 (1986), 937–946. [+]
A. Albanese, J. Bonet and W. J. Ricker, Mean ergodic operators in Fréchet spaces, Ann. Acad. Sci. Fenn. Math. 34 (2009), 401–436.

A. Aleman and L. Suciu, On ergodic operator means in Banach spaces, Integral Equations Operator Theory 85 (2016), 259–287.

I. Assani, Sur les opérateurs à puissances bornées et le théorème ergodique ponctuel dans Lp[0, 1], 1 < p < ∞, Canad. J. Math. 38 (1986), 937–946.

M. J. Beltrán-Meneu, Operators on Weighted Spaces of Holomorphic Functions, PhD Thesis, Universitat Politècnica de Valencia, Valencia, Spain, 2014.

M. J. Beltrán, J. Bonet and C. Fernández, Classical operators on weighted Banach spaces of entire functions, Proc. Amer. Math. Soc. 141 (2013), 4293–4303.

M. J. Beltrán, M.C. Gómez-Collado, E. Jordá and D. Jornet, Mean ergodic composition operators on Banach spaces of holomorphic functions, J. Funct. Anal. 270 (2016), 4369–4385.

N. C. Bernardes, Jr., A. Bonilla, V. Müller and A. Peris, Distributional chaos for linear operators, J. Funct. Anal. 265 (2013), 2143–2163.

N. C. Bernardes, Jr., A. Bonilla, A. Peris and X. Wu, Distributional chaos for operators in Banach spaces, J. Math. Anal. Appl. 459 (2018), 797–821.

J. Bonet, Dynamics of the differentiation operator on weighted spaces of entire functions, Math. Z. 261 (2009), 649–657.

Y. Derriennic, On the mean ergodic theorem for Cesaro bounded operators, Colloq. Math. 84/85 (2000), 443–455.

Y. Derriennic and M. Lin, On invariant measures and ergodic theorems for positive operators, J. Funct. Anal. 13 (1973), 252–267.

R. Émilion, Mean-bounded operators and mean ergodic theorems, J. Funct. Anal. 61 (1985), 1–14.

A. Gomilko and J. Zemánek, On the uniform Kreiss resolvent condition, (Russian) Funktsional. Anal. i Prilozhen. 42 (2008), 81–84

A. Gomilko and J. Zemánek, English translation in Funct. Anal. Appl. 42 (2008), 230–233.

K.-G. Grosse-Erdmann and A. Peris, Linear Chaos, Springer, London, 2011.

B. Z. Guo and H. Zwart, On the relation between stability of continuous- and discrete-time evolution equations via the Cayley transform, Integral Equations Operator Theory 54 (2006), 349–383.

B. Hou and L. Luo, Some remarks on distributional chaos for bounded linear operators, Turk. J. Math. 39 (2015), 251–258.

E. Hille, Remarks on ergodic theorems, Trans. Amer. Math. Soc. 57 (1945), 246–269.

I. Kornfeld and W. Kosek, Positive L1operators associated with nonsingular mappings and an example of E. Hille, Colloq. Math. 98 (2003), 63–77.

W. Kosek, Example of a mean ergodic L1operator with the linear rate of growth, Colloq. Math. 124 (2011), 15–22.

U. Krengel, Ergodic Theorems, Walter de Gruyter, Berlin, 1985.

C. Lubich and O. Nevanlinna, On resolvent conditions and stability estimates, BIT, 31 (1991), 293–313.

C. A. McCarthy, A Strong Resolvent Condition does not Imply Power-Boundedness, Chalmers Institute of Technology and the University of Göteborg, Preprint No. 15 (1971).

A. Montes-Rodríguez, J. Sánchez-Álvarez and J. Zemánek, Uniform Abel—Kreiss boundedness and the extremal behavior of the Volterra operator, Proc. London Math. Soc. 91 (2005), 761–788.

V. Müller and J. Vrsovsky, Orbits of linear operators tending to infinity, Rocky Mountain J. Math. 39 (2009), 219–230.

O. Nevanlinna, Resolvent conditions and powers of operators, Studia Math. 145 (2001), 113–134.

J. Neveu, Mathematical Foundations of the Calculus of Probability, Holden-Day, San Francisco, Calif.-London-Amsterdam, 1965.

A. L. Shields, On Möbius Bounded operators, Acta Sci. Math. (Szeged) 40 (1978), 371–374.

J. C. Strikwerda and B. A. Wade, A survey of the Kreiss matrix theorem for power bounded families of matrices and its extensions, in Linear Operators, Polish Acad. Sci., Warsaw, 1997, pp. 339–360.

L. Suciu, Ergodic behaviors of the regular operator means, Banach J. Math. Anal. 11 (2017), 239–265.

L. Suciu and J. Zemánek, Growth conditions on Cesàro means of higher order, Acta Sci. Math (Szeged) 79 (2013), 545–581.

Y. Tomilov and J. Zemánek, A new way of constructing examples in operator ergodic theory, Math. Proc. Cambridge Philos. Soc. 137 (2004), 209–225.

J. A. Van Casteren, Boundedness properties of resolvents and semigroups of operators, in Linear Operators, Polish Acad. Sci. Inst. Math., Warsaw, 1997, pp. 59–74.

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