Abstract:
Let A be a Banach operator ideal and X be a Banach space. We undertake the study of the vector space of A-null sequences of Carl and Stephani on X, c0,A(X), from a unified point of view after we introduce a norm which makes it a Banach space. To give accurate results we consider local versions of the different types of accessibility of Banach operator ideals. We show that in the most common situations, when A is right-accessible for (ℓ1;X),c0,A(X) behaves much alike c0(X). When this is the case we give a geometric tensor product representation of c0,A(X). On the other hand, we show an example where the representation fails. Also, via a trace duality formula, we characterize the dual space of c0,A(X). We apply our results to study some problems related with the KA -approximation property giving a trace condition which is used to solve the remaining case (p=1) of a problem posed by Kim (2015). Namely, we prove that if a dual space has the K1 -approximation property then the space has the Ku,1 -approximation property. © 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
Registro:
Documento: |
Artículo
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Título: | On null sequences for Banach operator ideals, trace duality and approximation properties |
Autor: | Lassalle, S.; Turco, P. |
Filiación: | Departamento de Matemática, Universidad de San Andrés, Vito Dumas 284, (B1644BID), Victoria, Buenos Aires, Argentina IMAS – CONICET, Argentina IMAS - UBA - CONICET - Pab I, Facultad de Cs. Exactas y Naturales, Universidad de Buenos Aires, Buenos Aires, 1428, Argentina
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Palabras clave: | 46B45; Secondary: 46B28; 46B50; approximation properties; compact sets; null sequences; Operator ideals; Primary: 46B04 |
Año: | 2017
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Volumen: | 290
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Número: | 14-15
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Página de inicio: | 2308
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Página de fin: | 2321
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DOI: |
http://dx.doi.org/10.1002/mana.201600273 |
Título revista: | Mathematische Nachrichten
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Título revista abreviado: | Math. Nachr.
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ISSN: | 0025584X
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Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0025584X_v290_n14-15_p2308_Lassalle |
Referencias:
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Citas:
---------- APA ----------
Lassalle, S. & Turco, P.
(2017)
. On null sequences for Banach operator ideals, trace duality and approximation properties. Mathematische Nachrichten, 290(14-15), 2308-2321.
http://dx.doi.org/10.1002/mana.201600273---------- CHICAGO ----------
Lassalle, S., Turco, P.
"On null sequences for Banach operator ideals, trace duality and approximation properties"
. Mathematische Nachrichten 290, no. 14-15
(2017) : 2308-2321.
http://dx.doi.org/10.1002/mana.201600273---------- MLA ----------
Lassalle, S., Turco, P.
"On null sequences for Banach operator ideals, trace duality and approximation properties"
. Mathematische Nachrichten, vol. 290, no. 14-15, 2017, pp. 2308-2321.
http://dx.doi.org/10.1002/mana.201600273---------- VANCOUVER ----------
Lassalle, S., Turco, P. On null sequences for Banach operator ideals, trace duality and approximation properties. Math. Nachr. 2017;290(14-15):2308-2321.
http://dx.doi.org/10.1002/mana.201600273