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A note on lower semicontinuous smooth norms

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A note on lower semicontinuous smooth norms

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Guirao Sánchez, AJ.; Lissitsin, A.; Montesinos Santalucia, V. (2019). A note on lower semicontinuous smooth norms. Revista de la Real Academia de Ciencias Exactas Físicas y Naturales Serie A Matemáticas. 113(3):2081-2085. https://doi.org/10.1007/s13398-018-0602-0

Por favor, use este identificador para citar o enlazar este ítem: http://hdl.handle.net/10251/162583

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Title: A note on lower semicontinuous smooth norms
Author: Guirao Sánchez, Antonio José Lissitsin, A. Montesinos Santalucia, Vicente
UPV Unit: Universitat Politècnica de València. Departamento de Matemática Aplicada - Departament de Matemàtica Aplicada
Issued date:
Abstract:
[EN] In Fabian et al. (Arch Math (Basel) 78(6):459-464, 2002) it was proved that, if a Valdivia compact space K has property P a property defined in terms of the Gateaux differentiability of certain norms on C(K)then, under ...[+]
Subjects: Smooth norms , Corson and Valdivia compacta , Plichko spaces
Copyrigths: Cerrado
Source:
Revista de la Real Academia de Ciencias Exactas Físicas y Naturales Serie A Matemáticas. (issn: 1578-7303 )
DOI: 10.1007/s13398-018-0602-0
Publisher:
Springer-Verlag
Publisher version: https://doi.org/10.1007/s13398-018-0602-0
Project ID:
info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2013-2016/MTM2017-83262-C2-1-P/ES/ANALISIS COMPLEJO Y GEOMETRIA EN ESPACIOS DE BANACH/
info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2013-2016/MTM2017-83262-C2-2-P/ES/LA INTERACCION ENTRE GEOMETRIA Y TOPOLOGIA EN ESPACIOS DE BANACH. APLICACIONES./
info:eu-repo/grantAgreement/f SéNeCa//19368%2FPI%2F14/
info:eu-repo/grantAgreement/HM//IUT20-57/
info:eu-repo/grantAgreement/Estonian Research Council//PUTJD670/
Thanks:
We thank the referee for suggestions that helped to improve the preliminary version of the manuscript. The first-named author was supported by AEI/FEDER (project MTM2017-83262-C2-2-P of Ministerio de Economia y Competitividad), ...[+]
Type: Artículo

References

Fabian, M., Habala, P., Hájek, P., Montesinos, V., Zizler, V.: Banach Space Theory: The Basis for Linear and Nonlinear Analysis. Springer, New York (2011)

Fabian, M., Montesinos, V., Zizler, V.: Pointwise semicontinuous smooth norms. Arch. Math. (Basel) 78(6), 459–464 (2002)

Deville, R., Godefroy, G.: Some applications of projectional resolutions of identity. Proc. Lond. Math. Soc. 67, 183–199 (1993) [+]
Fabian, M., Habala, P., Hájek, P., Montesinos, V., Zizler, V.: Banach Space Theory: The Basis for Linear and Nonlinear Analysis. Springer, New York (2011)

Fabian, M., Montesinos, V., Zizler, V.: Pointwise semicontinuous smooth norms. Arch. Math. (Basel) 78(6), 459–464 (2002)

Deville, R., Godefroy, G.: Some applications of projectional resolutions of identity. Proc. Lond. Math. Soc. 67, 183–199 (1993)

Deville, R., Godefroy, G., Zizler, V.: Smoothness and Renormings of Banach Spaces, Pitman Monographs 64. Logman, London (1993)

Fremlin, D.H.: Consequences of Martin’s Axioms. Cambridge University Press, Cambridge (1984)

Hájek, P., Montesinos, V., Vanderwerff, J., Zizler, V.: Biorthogonal Systems in Banach Spaces, CMS 26. Springer, New York (2008)

Kalenda, O.: Valdivia compact spaces in topology and Banach space theory. Extr. Math. 15, 1–85 (2000)

Kunen, K.: A compact L-space under CH. Topol. Appl. 12, 283–287 (1981)

Talagrand, M.: Renormages de quelques $$C(K)$$ C ( K ) . Isr. J. Math. 54, 327–334 (1986)

Valdivia, M.: Resoluciones proyectivas del operador identidad y bases de Markushevich en ciertos espacios de Banach. RACSAM Rev. R. Acad. Cienc. Exactas Físicas y Naturales, Ser. A Mat. 84, 23–34 (1990)

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