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Please use this identifier to cite or link to this item: http://hdl.handle.net/10481/32024

Title: Norm-attaining compact operators
Authors: Martín Suárez, Miguel
Issue Date: 2013
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 Schauder basis. It now makes sense to discuss sufficient conditions on the domain or the range space to ensure that every compact linear operator between them can be approximated by norm attaining operators. We get several basic results in this line and mention some open problems.
Sponsorship: Supported by Spanish MICINN and FEDER project no. MTM2012-31755 and by Junta de Andaluc´ıa and FEDER grants FQM-185 and P09-FQM-4911.
Keywords: Banach space
Norm-attaining operators
Compact operators
Approximaciones property
strict convexity
URI: http://hdl.handle.net/10481/32024
Rights : Creative Commons Attribution-NonCommercial-NoDerivs 3.0 License
Appears in Collections:DAM - Artículos

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