- -

Mean ergodicity and spectrum of the Cesàro operator on weighted c0 spaces

RiuNet: Institutional repository of the Polithecnic University of Valencia

Share/Send to

Cited by

Statistics

Mean ergodicity and spectrum of the Cesàro operator on weighted c0 spaces

Show full item record

Albanese, AA.; Bonet Solves, JA.; Ricker, WJ. (2016). Mean ergodicity and spectrum of the Cesàro operator on weighted c0 spaces. Positivity. 20:761-803. https://doi.org/10.1007/s11117-015-0385-x

Por favor, use este identificador para citar o enlazar este ítem: http://hdl.handle.net/10251/138016

Files in this item

Item Metadata

Title: Mean ergodicity and spectrum of the Cesàro operator on weighted c0 spaces
Author: Albanese, Angela A. Bonet Solves, José Antonio Ricker, Werner J.
UPV Unit: Universitat Politècnica de València. Departamento de Matemática Aplicada - Departament de Matemàtica Aplicada
Issued date:
Abstract:
[EN] A detailed investigation is made of the continuity, the compactness and the spectrum of the Cesàro operator C acting on the weighted Banach sequence space c0(w) for a bounded, strictly positive weight w. New features ...[+]
Subjects: Cesàro operator , Weighted c0 space , Spectrum , Compact operator , Mean ergodic operator
Copyrigths: Reserva de todos los derechos
Source:
Positivity. (issn: 1385-1292 )
DOI: 10.1007/s11117-015-0385-x
Publisher:
Springer-Verlag
Publisher version: https://doi.org/10.1007/s11117-015-0385-x
Project ID:
info:eu-repo/grantAgreement/MINECO//MTM2013-43540-P/ES/METODOS DEL ANALISIS FUNCIONAL Y TEORIA DE OPERADORES/
info:eu-repo/grantAgreement/GVA//PROMETEOII%2F2013%2F013/ES/Análisis funcional, teoría de operadores y sus aplicaciones (AFUNTOP)/
info:eu-repo/grantAgreement/GVA//ACOMP%2F2015%2F186/
Thanks:
The research of the first two authors was partially supported by the Projects MTM2013-43540-P, GVA Prometeo II/2013/013 and ACOMP/2015/186 (Spain).
Type: Artículo

References

Akhmedov, A.M., Başar, F.: On the fine spectrum of the Cesàro operator in $$c_0$$ c 0 . Math. J. Ibaraki Univ. 36, 25–32 (2004)

Akhmedov, A.M., Başar, F.: The fine spectrum of the Cesàro operator $$C_1$$ C 1 over the sequence space $$bv_p, (1 \le p < \infty ) $$ b v p , ( 1 ≤ p < ∞ ) . Math. J. Okayama Univ. 50, 135–147 (2008)

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) [+]
Akhmedov, A.M., Başar, F.: On the fine spectrum of the Cesàro operator in $$c_0$$ c 0 . Math. J. Ibaraki Univ. 36, 25–32 (2004)

Akhmedov, A.M., Başar, F.: The fine spectrum of the Cesàro operator $$C_1$$ C 1 over the sequence space $$bv_p, (1 \le p < \infty ) $$ b v p , ( 1 ≤ p < ∞ ) . Math. J. Okayama Univ. 50, 135–147 (2008)

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)

Albanese, A.A., Bonet, J., Ricker, W.J.: Spectrum and compactness of the Cesàro operator on weighted $$\ell _p$$ ℓ p spaces. J. Aust. Math. Soc. 99, 287–314 (2015)

Albanese, A.A., Bonet, J., Ricker, W.J.: The Cesàro operator in the Fréchet spaces $$\ell ^{p+}$$ ℓ p + and $$L ^{p-}$$ L p - . Glasg. Math. J (to appear)

Ansari, S.I., Bourdon, P.S.: Some properties of cyclic operators. Acta Sci. Math. Szeged 63, 195–207 (1997)

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

Curbera, G.P., Ricker, W.J.: Spectrum of the Cesàro operator in $$\ell ^p$$ ℓ p . Arch. Math. 100, 267–271 (2013)

Curbera, G.P., Ricker, W.J.: Solid extensions of the Cesàro operator on $$\ell ^p$$ ℓ p and $$c_0$$ c 0 . Integr. Equ. Oper. Theory 80, 61–77 (2014)

Curbera, G.P., Ricker, W.J.: The Cesàro operator and unconditional Taylor series in Hardy spaces. Integr. Equ. Oper. Theory 83, 179–195 (2015)

Diestel, J.: Sequences and Series in Banach Spaces. Springer, New York (1984)

Dowson, H.R.: Spectral Theory of Linear Operators. Academic Press, London (1978)

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

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

Goldberg, S.: Unbounded Linear Operators: Theory and Applications. Dover Publ, New York (1985)

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

Jarchow, H.: Locally Convex Spaces. Teubner, Stuttgart (1981)

Krengel, U.: Ergodic Theorems. de Gruyter, Berlin (1985)

Leibowitz, G.: Spectra of discrete Cesàro operators. Tamkang J. Math. 3, 123–132 (1972)

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

Megginson, R.E.: An Introduction to Banach Space Theory. Springer, New York (1998)

Mureşan, M.: A Concrete Approach to Classical Analysis. Springer, Berlin (2008)

Okutoyi, J.I.: On the spectrum of $$C_1$$ C 1 as an operator on $$bv_0$$ b v 0 . J. Aust. Math. Soc. Ser. A 48, 79–86 (1990)

Radjavi, H., Tam, P.-W., Tan, K.-K.: Mean ergodicity for compact operators. Studia Math. 158, 207–217 (2003)

Reade, J.B.: On the spectrum of the Cesàro operator. Bull. Lond. Math. Soc. 17, 263–267 (1985)

Rhoades, B.E., Yildirim, M.: The spectra and fine spectra of factorable matrices on $$c_0$$ c 0 . Math. Commun. 16, 265–270 (2011)

Taylor, A.E.: Introduction to Functional Analysis. Wiley, New York (1958)

[-]

recommendations

 

This item appears in the following Collection(s)

Show full item record