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The Cesàro operator on Korenblum type spaces of analytic functions

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The Cesàro operator on Korenblum type spaces of analytic functions

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Albanese, A.; Bonet Solves, JA.; Ricker, WJ. (2018). The Cesàro operator on Korenblum type spaces of analytic functions. Collectanea mathematica. 69(2):263-281. https://doi.org/10.1007/s13348-017-0205-7

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Title: The Cesàro operator on Korenblum type spaces of analytic functions
Author: Albanese, Angela Bonet Solves, José Antonio Ricker, Werner J.
UPV Unit: Universitat Politècnica de València. Departamento de Matemática Aplicada - Departament de Matemàtica Aplicada
Issued date:
Embargo end date: 2019-05-01
Abstract:
[EN] The spectrum of the CesA ro operator , which is always continuous (but never compact) when acting on the classical Korenblum space and other related weighted Fr,chet or (LB) spaces of analytic functions on the open ...[+]
Subjects: Cesaro operator , Weighted spaces of analytic functions , Spectrum , Frechet spaces , (LB)-spaces , Mean ergodicity
Copyrigths: Reserva de todos los derechos
Source:
Collectanea mathematica. (issn: 0010-0757 )
DOI: 10.1007/s13348-017-0205-7
Publisher:
Springer-Verlag
Publisher version: http://doi.org/10.1007/s13348-017-0205-7
Project ID:
AEI/MTM2016-76647-P
info:eu-repo/grantAgreement/MINECO//MTM2013-43540-P/ES/METODOS DEL ANALISIS FUNCIONAL Y TEORIA DE OPERADORES/
Thanks:
The research of the first two authors was partially supported by the projects MTM2013-43540-P and MTM2016-76647-P. The second author gratefully acknowledges the support of the Alexander von Humboldt Foundation.
Type: Artículo

References

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.: Montel resolvents and uniformly mean ergodic semigroups of linear operators. Quaest. Math. 36, 253–290 (2013)

Albanese, A.A., Bonet, J., Ricker, W.J.: The Cesàro operator in growth Banach spaces of analytic functions. Integral Equ. Oper. Theory 86, 97–112 (2016) [+]
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.: Montel resolvents and uniformly mean ergodic semigroups of linear operators. Quaest. Math. 36, 253–290 (2013)

Albanese, A.A., Bonet, J., Ricker, W.J.: The Cesàro operator in growth Banach spaces of analytic functions. Integral Equ. Oper. Theory 86, 97–112 (2016)

Albanese, A.A., Bonet, J., Ricker, W.J.: The Cesàro operator in the Fréchet spaces $$\ell ^{p+}$$ ℓ p + and $$L^{p-}$$ L p - . Glasgow Math. J. 59, 273–287 (2017)

Albanese, A.A., Bonet, J., Ricker, W.J.: The Cesàro operator on power series spaces. Stud. Math. doi: 10.4064/sm8590-2-2017

Aleman, A.: A class of integral operators on spaces of analytic functions, In: Proceedings of the Winter School in Operator Theory and Complex Analysis, Univ. Málaga Secr. Publ., Málaga, pp. 3–30 (2007)

Aleman, A., Constantin, O.: Spectra of integration operators on weighted Bergman spaces. J. Anal. Math. 109, 199–231 (2009)

Aleman, A., Peláez, J.A.: Spectra of integration operators and weighted square functions. Indiana Univ. Math. J. 61, 1–19 (2012)

Aleman, A., Persson, A.-M.: Resolvent estimates and decomposable extensions of generalized Cesàro operators. J. Funct. Anal. 258, 67–98 (2010)

Aleman, A., Siskakis, A.G.: An integral operator on $$H^p$$ H p . Complex Var. Theory Appl. 28, 149–158 (1995)

Aleman, A., Siskakis, A.G.: Integration operators on Bergman spaces. Indiana Univ. Math. J. 46, 337–356 (1997)

Barrett, D.E.: Duality between $$A^\infty $$ A ∞ and $$A^{- \infty }$$ A - ∞ on domains with nondegenerate corners, Multivariable operator theory (Seattle, WA, 1993), pp. 77–87, Contemporary Math. Vol. 185, Amer. Math. Soc., Providence (1995)

Bierstedt, K.D., Bonet, J., Galbis, A.: Weighted spaces of holomorphic functions on bounded domains. Mich. Math. J. 40, 271–297 (1993)

Bierstedt, K.D., Bonet, J., Taskinen, J.: Associated weights and spaces of holomorphic functions. Stud. Math. 127, 137–168 (1998)

Bierstedt, K.D., Meise, R., Summers, W.H.: A projective description of weighted inductive limits. Trans. Am. Math. Soc. 272, 107–160 (1982)

Bierstedt, K.D., Summers, W.H.: Biduals of weighted Banach spaces of analytic functions. J. Aust. Math. Soc. (Ser. A) 54, 70–79 (1993)

Bonet, J., Domański, P., Lindström, M., Taskinen, J.: Composition operators between weighted Banach spaces of analytic functions. J. Aust. Math. Soc. (Ser. A) 64, 101–118 (1998)

Diestel, J., Jarchow, H., Tonge, A.: Absolutely Summing Operators. Cambridge University Press, Cambridge (1995)

Domenig, T.: Composition operators on weighted Bergman spaces and Hardy spaces. Atomic Decompositions and Diagonal Operators, Ph.D. Thesis, University of Zürich (1997). [Zbl 0909.47025]

Domenig, T.: Composition operators belonging to operator ideals. J. Math. Anal. Appl. 237, 327–349 (1999)

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

Edwards, R.E.: Functional Analysis. Theory and Applications. Holt, Rinehart and Winston, New York, Chicago San Francisco (1965)

Grothendieck, A.: Topological Vector Spaces. Gordon and Breach, London (1973)

Hedenmalm, H., Korenblum, B., Zhu, K.: Theory of Bergman Spaces. Graduate Texts in Mathematics, vol. 199. Springer, New York (2000)

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

Korenblum, B.: An extension of the Nevanlinna theory. Acta Math. 135, 187–219 (1975)

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

Lusky, W.: On the isomorphism classes of weighted spaces of harmonic and holomorphic functions. Stud. Math. 175(1), 19–40 (2006)

Meise, R., Vogt, D.: Introduction to Functional Analysis. Clarendon Press, Oxford (1997)

Melikhov, S.N.: (DFS )-spaces of holomorphic functions invariant under differentiation. J. Math. Anal. Appl. 297, 577–586 (2004)

Persson, A.-M.: On the spectrum of the Cesàro operator on spaces of analytic functions. J. Math. Anal Appl. 340, 1180–1203 (2008)

Pietsch, A.: Nuclear Locally Convex Spaces. Springer, Berlin (1972)

Shields, A.L., Williams, D.L.: Bounded projections, duality and multipliers in spaces of analytic functions. Trans. Am. Math. Soc. 162, 287–302 (1971)

Siskakis, A.: Volterra operators on spaces of analytic functions—a survey. In: Proceedings of the First Advanced Course in Operator Theory and Complex Analysis, Univ. Sevilla Serc. Publ., Seville, pp. 51–68 (2006)

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