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# Distance formulas on weighted Banach spaces of analytic functions

Bonet Solves, JA.; Lusky, W.; Taskinen, J. (2019). Distance formulas on weighted Banach spaces of analytic functions. Complex Analysis and Operator Theory. 13(3):893-900. https://doi.org/10.1007/s11785-018-0815-4

Por favor, use este identificador para citar o enlazar este ítem: http://hdl.handle.net/10251/155435

## Files in this item

Title: Distance formulas on weighted Banach spaces of analytic functions
Author:
UPV Unit: Universitat Politècnica de València. Departamento de Matemática Aplicada - Departament de Matemàtica Aplicada
Issued date:
 2019-04
Abstract:
[EN] Let v be a radial weight function on the unit disc or on the complex plane. It is shown that for each analytic function f0 in the Banach space Hv all analytic functions f such that v|f| is bounded, the distance of f0 ...[+]
Subjects:
Copyrigths: Reserva de todos los derechos
Source:
Complex Analysis and Operator Theory. (issn: 1661-8254 )
DOI: 10.1007/s11785-018-0815-4
Publisher:
Springer-Verlag
Publisher version: https://doi.org/10.1007/s11785-018-0815-4
Project ID:
AGENCIA ESTATAL DE INVESTIGACION/MTM2016-76647-P
GENERALITAT VALENCIANA/PROMETEO/2017/102
Thanks:
The authors are very thankful to the referees for their careful reading of the manuscript and their suggestions. The research of Bonet was partially supported by the Projects MTM2016-76647-P and GV Prometeo 2017/102. The ...[+]
Type: Artículo

## References

Axler, S., Berg, I.D., Jewell, N., Shields, A.: Approximation by compact operators and the space $$H^{\infty }+C$$ H ∞ + C . Ann. Math. 109, 601–612 (1979)

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. Studia Math. 127, 137–168 (1998) [+]
Axler, S., Berg, I.D., Jewell, N., Shields, A.: Approximation by compact operators and the space $$H^{\infty }+C$$ H ∞ + C . Ann. Math. 109, 601–612 (1979)

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. Studia Math. 127, 137–168 (1998)

Holmes, R., Scranton, B., Ward, J.: Approximation from the space of compact operators and other M-ideals. Duke Math. J. 42, 259–269 (1975)

Lusky, W.: On the Fourier series of unbounded harmonic functions. J. Lond. Math. Soc. 2(61), 568–580 (2000)

Lusky, W.: On the isomorphism classes of weighted spaces of harmonic and holomorphic functions. Studia Math. 175, 19–45 (2006)

Perfekt, K.-M.: Duality and distance formulas in spaces defined by means of oscillation. Ark. Mat. 51, 345–361 (2013)

Perfekt, K.-M.: On M-ideals and o–O type spaces. Math. Scand. 121(1), 151–160 (2017)

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

Tjani, M.: Distance of a Bloch function to the little Bloch space. Bull. Aust. Math. Soc. 74, 101–119 (2006)

Yuan, C., Tong, C.: Distance from Bloch-type functions to the analytic space $$F(p,q,s)$$ F ( p , q , s ) , Abstr. Appl. Anal. 2014, article ID 610237

Zhu, K.: Operator Theory in Function Spaces, 2nd edn. American Mathematical Society, Providence (2007)

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