dc.contributor.author |
Angosto Hernández, Carlos
|
es_ES |
dc.contributor.author |
Kakol, Jerzy
|
es_ES |
dc.contributor.author |
Kubzdela, Albert
|
es_ES |
dc.contributor.author |
López Pellicer, Manuel
|
es_ES |
dc.date.accessioned |
2014-06-04T07:26:06Z |
|
dc.date.issued |
2013-05 |
|
dc.identifier.issn |
0003-889X |
|
dc.identifier.uri |
http://hdl.handle.net/10251/37911 |
|
dc.description.abstract |
For a Banach space E and its bidual space E'', the function k(H) defined on bounded
subsets H of E measures how far H is from being σ(E,E')-relatively compact in E. This concept, introduced independently by Granero, and Cascales et al., has been used to study a quantitative version of Krein¿s theorem for Banach spaces E and spaces Cp(K) over compact K. In the present paper, a quantitative version of Krein¿s theorem on
convex envelopes coH of weakly compact sets H is proved for Fréchet spaces, i.e. metrizable and complete locally convex spaces. For a Fréchet space E, the above function k(H) has been defined in thisi paper by menas of d(h,E) is the natural distance of h to E in the bidual E''. The main result of the paper is the following theorem: For
a bounded set H in a Fréchet space E, the following inequality holds
k(coH) < (2^(n+1) − 2)k(H) + 1/2^n for all n ∈ N. Consequently, this yields
also the following formula k(coH) ≤ (k(H))^(1/2))(3-2(k(H)^(1/2))). Hence coH is
weakly relatively compact provided H is weakly relatively compact in E.
This extends a quantitative version of Krein¿s theorem for Banach spaces
(obtained by Fabian, Hajek, Montesinos, Zizler, Cascales, Marciszewski,
and Raja) to the class of Fréchet spaces. We also define and discuss two
other measures of weak non-compactness lk(H) and k'(H) for a Fréchet
space and provide two quantitative versions of Krein¿s theorem for both
functions. |
es_ES |
dc.description.sponsorship |
The research was supported for C. Angosto by the project MTM2008-05396 of the Spanish Ministry of Science and Innovation, for J. Kakol by National Center of Science, Poland, Grant No. N N201 605340, and for M. Lopez-Pellicer by the project MTM2010-12374-E (complementary action) of the Spanish Ministry of Science and Innovation. |
en_EN |
dc.language |
Inglés |
es_ES |
dc.publisher |
Springer Verlag (Germany) |
es_ES |
dc.relation.ispartof |
Archiv der Mathematik |
es_ES |
dc.rights |
Reserva de todos los derechos |
es_ES |
dc.subject |
Krein's theorem |
es_ES |
dc.subject |
Compactness |
es_ES |
dc.subject |
Fréchet space |
es_ES |
dc.subject |
Space of continuous functions |
es_ES |
dc.subject.classification |
MATEMATICA APLICADA |
es_ES |
dc.title |
A quantitative version of Krein's theorems for Fréchet spaces |
es_ES |
dc.type |
Artículo |
es_ES |
dc.embargo.lift |
10000-01-01 |
|
dc.embargo.terms |
forever |
es_ES |
dc.identifier.doi |
10.1007/s00013-013-0513-4 |
|
dc.relation.projectID |
info:eu-repo/grantAgreement/MICINN//MTM2008-05396/ES/LA INTERACCION ENTRE TEORIA DE LA MEDIDA, TOPOLOGIA Y ANALISIS FUNCIONAL/ |
|
dc.relation.projectID |
info:eu-repo/grantAgreement/NCN//N N201 605340/ |
|
dc.relation.projectID |
info:eu-repo/grantAgreement/MICINN//MTM2010-12374-E/ES/ESTRATEGIAS PARA EL PROGRESO MATEMATICO EN ESPAÑA/ |
|
dc.rights.accessRights |
Abierto |
es_ES |
dc.contributor.affiliation |
Universitat Politècnica de València. Departamento de Matemática Aplicada - Departament de Matemàtica Aplicada |
es_ES |
dc.description.bibliographicCitation |
Angosto Hernández, C.; Kakol, J.; Kubzdela, A.; López Pellicer, M. (2013). A quantitative version of Krein's theorems for Fréchet spaces. Archiv der Mathematik. 101(1):65-77. https://doi.org/10.1007/s00013-013-0513-4 |
es_ES |
dc.description.accrualMethod |
S |
es_ES |
dc.relation.publisherversion |
http://link.springer.com/content/pdf/10.1007%2Fs00013-013-0513-4.pdf |
es_ES |
dc.description.upvformatpinicio |
65 |
es_ES |
dc.description.upvformatpfin |
77 |
es_ES |
dc.type.version |
info:eu-repo/semantics/publishedVersion |
es_ES |
dc.description.volume |
101 |
es_ES |
dc.description.issue |
1 |
es_ES |
dc.relation.senia |
246301 |
|
dc.contributor.funder |
Ministerio de Ciencia e Innovación |
|
dc.contributor.funder |
National Science Centre, Polonia |
|
dc.description.references |
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es_ES |
dc.description.references |
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es_ES |
dc.description.references |
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es_ES |
dc.description.references |
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es_ES |
dc.description.references |
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es_ES |
dc.description.references |
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es_ES |
dc.description.references |
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es_ES |
dc.description.references |
M. Fabian et al. Functional Analysis and Infinite-dimensional geometry, CMS Books in Mathematics, Canadian Math. Soc., Springer (2001). |
es_ES |
dc.description.references |
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es_ES |
dc.description.references |
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es_ES |
dc.description.references |
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es_ES |
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es_ES |
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es_ES |