Cascales, B.; Guirao Sánchez, AJ.; Kadets, V. (2013). A Bishop-Phelps-Bollobas Type Theorem for uniform algegras. Advances in Mathematics. 240:370-382. https://doi.org/10.1016/j.aim.2013.03.005
Por favor, use este identificador para citar o enlazar este ítem: http://hdl.handle.net/10251/37716
Title:
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A Bishop-Phelps-Bollobas Type Theorem for uniform algegras
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Author:
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Cascales, B.
Guirao Sánchez, Antonio José
Kadets, V.
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UPV Unit:
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Universitat Politècnica de València. Departamento de Matemática Aplicada - Departament de Matemàtica Aplicada
Universitat Politècnica de València. Instituto Universitario de Matemática Pura y Aplicada - Institut Universitari de Matemàtica Pura i Aplicada
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Issued date:
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Abstract:
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This paper is devoted to showing that Asplund operators with range in a uniform Banach algebra have
the Bishop¿Phelps¿Bollobas property, i.e., they are approximated by norm attaining Asplund operators
at the same time ...[+]
This paper is devoted to showing that Asplund operators with range in a uniform Banach algebra have
the Bishop¿Phelps¿Bollobas property, i.e., they are approximated by norm attaining Asplund operators
at the same time that a point where the approximated operator almost attains its norm is approximated
by a point at which the approximating operator attains it. To prove this result we use the weak*-to-norm
fragmentability of weak*-compact subsets of the dual of Asplund spaces and we need to observe a Urysohn type result producing peak complex-valued functions in uniform algebras that are small outside a given open set and whose image is inside a Stolz region.
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Subjects:
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Bishop-Phelps-Bollobás
,
Asplund operators
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Norm attaining
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Uniform
Banach algebra
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Peak functions
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Urysohn lemma
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IUMPA
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Copyrigths:
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Reserva de todos los derechos
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Source:
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Advances in Mathematics. (issn:
0001-8708
)
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DOI:
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10.1016/j.aim.2013.03.005
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Publisher:
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Elsevier
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Publisher version:
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http://dx.doi.org/10.1016/j.aim.2013.03.005
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Project ID:
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info:eu-repo/grantAgreement/MICINN//MTM2008-05396/ES/LA INTERACCION ENTRE TEORIA DE LA MEDIDA, TOPOLOGIA Y ANALISIS FUNCIONAL/ /
info:eu-repo/grantAgreement/GVA//GV%2F2010%2F036/
info:eu-repo/grantAgreement/UPV//PAID-06-09-2829/
info:eu-repo/grantAgreement/MICINN//MTM2011-25377/ES/LA INTERACCION ENTRE TEORIA DE LA MEDIDA, TOPOLOGIA Y ANALISIS FUNCIONAL./
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Thanks:
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This research was partially supported by MEC and FEDER projects MTM2008-05396 and MTM2011-25377. The research of the second author was also partially supported by Generalitat Valenciana (GV/2010/036), and by Universidad ...[+]
This research was partially supported by MEC and FEDER projects MTM2008-05396 and MTM2011-25377. The research of the second author was also partially supported by Generalitat Valenciana (GV/2010/036), and by Universidad Politecnica de Valencia (project PAID-06-09-2829).
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Type:
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Artículo
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