Norm-attaining compact operators

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

Cited by in corpus (7)

• The Bishop-Phelps-Bollobás property for operators on $C(K)$
• The version for compact operators of Lindenstrauss properties A and B
• Residuality in the set of norm attaining operators between Banach spaces
• Numerical radius attaining compact linear operators
• Stability results of properties related to the Bishop-Phelps-Bollobás property for operators
• Approximate Birkhoff-James orthogonality and smoothness in the space of bounded linear operators
• Weak-star quasi norm attaining operators