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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
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
Palabras clave:46B45; Secondary: 46B28; 46B50; approximation properties; compact sets; null sequences; Operator ideals; Primary: 46B04
Año:2017
Volumen:290
Número:14-15
Página de inicio:2308
Página de fin:2321
DOI: http://dx.doi.org/10.1002/mana.201600273
Título revista:Mathematische Nachrichten
Título revista abreviado:Math. Nachr.
ISSN:0025584X
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0025584X_v290_n14-15_p2308_Lassalle

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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