Name: Norm-attaining compact operators
Creator: Miguel Martín
Keywords: Mathematics - Functional Analysis, Banach space, Primary 46B20, Secondary 46B04, 46B45, 46B28, 47B07, Compact operators, Norm-attaining operators, Approximaciones property, FOS: Mathematics, 0101 mathematics, 10. No inequality, 01 natural sciences

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Sep 2014Embargo end date: 01 Jan 2013 English Publisher:Elsevier BVJournal:Journal of Functional Analysis, volume 267, pages 1,585-1,592 (issn: 0022-1236,

Authors: Miguel Martín;

doi: 10.1016/j.jfa.2014.05.019 , 10.48550/arxiv.1306.1155

arXiv: http://arxiv.org/abs/1306.1155

handle: 10481/32024

Norm-attaining compact operators

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Abstract

We show examples of compact linear operators between Banach spaces which cannot be approximated by norm attaining operators. This is the negative answer to an open question posed in the 1970's. Actually, any strictly convex Banach space failing the approximation property serves as the range space. On the other hand, there are examples in which the domain space has a Schauder basis.

To appear in J. Funct. Anal. Section 3 of previous version has been removed

Related Organizations

University of Granada
Spain

Keywords

Mathematics - Functional Analysis, Banach space, Primary 46B20, Secondary 46B04, 46B45, 46B28, 47B07, Compact operators, Norm-attaining operators, Approximaciones property, FOS: Mathematics, strict convexity, Functional Analysis (math.FA)

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