- -

Operators acting in sequence spaces generated by dual Banach spaces of discrete Cesàro spaces

RiuNet: Repositorio Institucional de la Universidad Politécnica de Valencia

Compartir/Enviar a

Citas

Estadísticas

  • Estadisticas de Uso

Operators acting in sequence spaces generated by dual Banach spaces of discrete Cesàro spaces

Mostrar el registro completo del ítem

Bonet Solves, JA.; Ricker, WJ. (2021). Operators acting in sequence spaces generated by dual Banach spaces of discrete Cesàro spaces. Functiones et Approximatio Commentarii Mathematici. 64(1):109-139. https://doi.org/10.7169/facm/1907

Por favor, use este identificador para citar o enlazar este ítem: http://hdl.handle.net/10251/183894

Ficheros en el ítem

Metadatos del ítem

Título: Operators acting in sequence spaces generated by dual Banach spaces of discrete Cesàro spaces
Autor: Bonet Solves, José Antonio Ricker, Werner J.
Entidad UPV: Universitat Politècnica de València. Departamento de Matemática Aplicada - Departament de Matemàtica Aplicada
Fecha difusión:
Resumen:
[EN] The dual spaces d(p), 1 < p < infinity, of the discrete Cesaro (Banach) spaces ces(q), 1 < q < infinity, were studied by G. Bennett, A. Jagers and others. These (reflexive) dual Banach spaces induce the non-normable ...[+]
Palabras clave: Fréchet sequence space , (LB)-space , Spectrum , Multiplication operator , Cesàro operator , Mean ergodic operator
Derechos de uso: Cerrado
Fuente:
Functiones et Approximatio Commentarii Mathematici. (issn: 0208-6573 )
DOI: 10.7169/facm/1907
Editorial:
Adam Mickiewicz University
Versión del editor: https://doi.org/10.7169/facm/1907
Código del Proyecto:
info:eu-repo/grantAgreement/AGENCIA ESTATAL DE INVESTIGACION//MTM2016-76647-P//ANALISIS FUNCIONAL, TEORIA DE OPERADORES Y ANALISIS TIEMPO-FRECUENCIA/
info:eu-repo/grantAgreement/GENERALITAT VALENCIANA//PROMETEO%2F2017%2F102//ANALISIS FUNCIONAL, TEORIA DE OPERADORES Y APLICACIONES./
Agradecimientos:
The research of J. Bonet was partially supported by the projects MTM2016-76647-P and GV Prometeo/2017/102 (Spain).
Tipo: Artículo

References

[1] A.A. Albanese, J. Bonet, W.J. Ricker, <i>Montel resolvents and uniformly mean ergodic semigroups of linear operators,</i> Quaest. Math. <b>36</b> (2013), 253–290.

[2] A.A. Albanese, J. Bonet, W.J. Ricker, <i>The Cesàro operator in the Fréchet spaces $ \ell^{p+}$ and $ L^{p-}$,</i> Glasgow Math. J. <b>59</b> (2017), 273–287.

[4] A.A. Albanese, J. Bonet, W.J. Ricker, <i>The Cesàro operator on Korenblum type spaces of analytic functions,</i> Collect. Math. <b>69</b> (2018), 263–281. [+]
[1] A.A. Albanese, J. Bonet, W.J. Ricker, <i>Montel resolvents and uniformly mean ergodic semigroups of linear operators,</i> Quaest. Math. <b>36</b> (2013), 253–290.

[2] A.A. Albanese, J. Bonet, W.J. Ricker, <i>The Cesàro operator in the Fréchet spaces $ \ell^{p+}$ and $ L^{p-}$,</i> Glasgow Math. J. <b>59</b> (2017), 273–287.

[4] A.A. Albanese, J. Bonet, W.J. Ricker, <i>The Cesàro operator on Korenblum type spaces of analytic functions,</i> Collect. Math. <b>69</b> (2018), 263–281.

[8] S.V. Astashkin, L. Maligranda, <i>Structure of Cesàro function spaces: a survey,</i> Function Spaces X, pp. 13–40. Banach Center Publ. <b>102</b>, Polish Acad. Sci. Inst. Math., Warsaw, 2014.

[9] G. Bennett, <i>Factorizing the classical inequalities,</i> Mem. Amer. Math. Soc. <b>120</b> (576), 1996, 1–130.

[10] J. Bonet, W.J. Ricker, <i>Operators acting in the dual spaces of discrete Cesàro spaces,</i> Monatsh. Math. <b>191</b> (2020), 487–512.

[11] J. Bonet, W.J. Ricker, <i>Fréchet and (LB) sequence spaces induced by dual Banach spaces of discrete Cesàro spaces,</i> Bull. Belg. Math. Soc. Simon Stevin (to appear), arXiv: 2009.01132v1.

[12] P.S. Bourdon, N.S. Feldman, J.H. Shapiro, <i>Some properties of $N$-supercyclic operators,</i> Studia Math., <b>165</b> (2004), 135–157.

[13] G. Crofts, <i>Concerning perfect Fréchet spaces and diagonal transformations,</i> Math. Ann. <b>182</b> (1969), 67–76.

[14] G.P. Curbera, W.J. Ricker, <i>Solid extensions of the Cesàro operator on $\ell^p$ and $ c_0$,</i> Integral Equ. Oper. Theory <b>80</b> (2014), 61–77.

[15] R.E. Edwards, <i>Functional Analysis. Theory and Applications,</i> Holt, Rinehart and Winston, New York-Chicago-San Fransisco, 1965.

[16] K.-G. Grosse-Erdmann, <i>The Blocking Technique, Weighted Mean Operators and Hardy's Inequality,</i> Lecture Notes in Math., vol. <b>1679</b>, Springer Verlag, Berlin Heidelberg, 1998.

[17] A. Grothendieck, <i>Topological Vector Spaces,</i> Gordon and Breach, London, 1973.

[18] G.H. Hardy, J.E. Littlewood, G. Pólya, <i>Inequalities,</i> Cambridge University Press, Cambridge, 1934.

[19] A.A. Jagers, <i>A note on Cesàro sequence spaces,</i> Nieuw, Arch. Wisk. <b>22</b> (1974), 113–124.

[20] H. Jarchow, <i>Locally Convex Spaces,</i> Teubner, Stuttgart, 1981.

[21] G. Köthe, <i>Topological Vector Spaces I,</i> 2nd printing rev., Springer, New York, 1983.

[22] G. Köthe, <i>Topological Vector Spaces II,</i> Springer, Berlin, 1979.

[23] U. Krengel, <i>Ergodic Theorems,</i> de Gruyter Studies in Mathematics <b>6</b>, Walter de Gruyter Co., Berlin, 1985.

[24] K. Leśnik, L. Maligranda, <i>Abstract Cesàro spaces. Duality,</i> J. Math. Anal. Appl. <b>424</b> (2015), 932–951.

[25] R. Meise, D. Vogt, <i>Introduction to Functional Analysis,</i> Clarendon Press, Oxford, 1997.

[26] A. Rodriguez-Arenas, <i>Some results about diagonal operators on Köthe echelon spaces,</i> Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Math. RACSAM <b>113</b> (2019), 2959–2968.

[27] A.E. Taylor, <i>Introduction to Functional Analysis,</i> Wiley International Edition, John Wiley &amp; Sons, Tokyo, 1958.

[28] L. Waelbroeck, <i>Topological Vector Spaces and Algebras,</i> Lecture Notes in Math., vol. <b>230</b>, Springer, Berlin, 1971.

[3] A.A. Albanese, J. Bonet, W.J. Ricker, <i>The Fréchet spaces $\mathrm{ces} (p+), 1 \leq p \lt \infty$,</i> J. Math. Anal. Appl. <b>458</b> (2018), 1314–1323.

[5] A.A. Albanese, J. Bonet, W.J. Ricker, <i>Operators on the Fréchet sequence spaces $\mathrm{ces} (p+), 1 ≤ p \lt \infty$,</i> Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM <b>113</b> (2019), 1533–1556.

[6] A.A. Albanese, J. Bonet, W.J. Ricker, <i>Multiplier and averaging operators in the Banach spaces $\mathrm{ces}(p), 1 \lt p \lt \infty$,</i> Positivity <b>23</b> (2019), 177–193.

[7] A.A. Albanese, J. Bonet, W.J. Ricker, <i>Linear operators on the (LB)-sequence spaces $\mathrm{ces} (p-), 1 \lt p ≤ \infty$,</i> Descriptive topology and functional analysis II, Springer, Cham, Proc. Math. Stat. <b>286</b> (2019), 43–67.

[-]

recommendations

 

Este ítem aparece en la(s) siguiente(s) colección(ones)

Mostrar el registro completo del ítem