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On null sequences for Banach operator ideals, trace duality and approximation properties

2017; Wiley; Volume: 290; Issue: 14-15 Linguagem: Inglês

10.1002/mana.201600273

1522-2616

Silvia Lassalle, Pablo Turco,

Holomorphic and Operator Theory

Mathematische NachrichtenVolume 290, Issue 14-15 p. 2308-2321 REVIEW ARTICLE On null sequences for Banach operator ideals, trace duality and approximation properties Silvia Lassalle, Corresponding Author Silvia Lassalle slassalle@udesa.edu.ar orcid.org/0000-0002-8471-0282 Departamento de Matemática, Universidad de San Andrés, Vito Dumas 284, (B1644BID) Victoria, Buenos Aires, Argentina and IMAS – CONICET Correspondence Silvia Lassalle, Departamento de Matemática, Universidad de San Andrés, Vito Dumas 284, (B1644BID) Victoria, Buenos Aires, Argentina and IMAS – CONICET. Email: slassalle@udesa.edu.arSearch for more papers by this authorPablo Turco, Pablo Turco IMAS - UBA - CONICET - Pab I, Facultad de Cs. Exactas y Naturales, Universidad de Buenos Aires, 1428 Buenos Aires, ArgentinaSearch for more papers by this author Silvia Lassalle, Corresponding Author Silvia Lassalle slassalle@udesa.edu.ar orcid.org/0000-0002-8471-0282 Departamento de Matemática, Universidad de San Andrés, Vito Dumas 284, (B1644BID) Victoria, Buenos Aires, Argentina and IMAS – CONICET Correspondence Silvia Lassalle, Departamento de Matemática, Universidad de San Andrés, Vito Dumas 284, (B1644BID) Victoria, Buenos Aires, Argentina and IMAS – CONICET. Email: slassalle@udesa.edu.arSearch for more papers by this authorPablo Turco, Pablo Turco IMAS - UBA - CONICET - Pab I, Facultad de Cs. Exactas y Naturales, Universidad de Buenos Aires, 1428 Buenos Aires, ArgentinaSearch for more papers by this author First published: 06 April 2017 https://doi.org/10.1002/mana.201600273Citations: 6Read the full textAboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Abstract Let be a Banach operator ideal and X be a Banach space. We undertake the study of the vector space of -null sequences of Carl and Stephani on 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 is right-accessible for , behaves much alike . When this is the case we give a geometric tensor product representation of . On the other hand, we show an example where the representation fails. Also, via a trace duality formula, we characterize the dual space of . We apply our results to study some problems related with the -approximation property giving a trace condition which is used to solve the remaining case () of a problem posed by Kim (2015). Namely, we prove that if a dual space has the -approximation property then the space has the -approximation property. Citing Literature Volume290, Issue14-15October 2017Pages 2308-2321 RelatedInformation