This is an announcement for the paper "Norm-attaining compact operators" by Miguel Martin.
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.
Archive classification: math.FA
Mathematics Subject Classification: Primary 46B20, Secondary 46B04, 46B45, 46B28, 47B07
Submitted from: mmartins@ugr.es
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1306.1155
or