Banach Journal of Mathematical Analysis
- Banach J. Math. Anal.
- Volume 10, Number 3 (2016), 621-637.
Norm-attaining Lipschitz functionals
We prove that for a given Banach space , the subset of norm-attaining Lipschitz functionals in is weakly dense but not strongly dense. Then we introduce a weaker concept of directional norm attainment and demonstrate that for a uniformly convex the set of directionally norm-attaining Lipschitz functionals is strongly dense in and, moreover, that an analogue of the Bishop–Phelps–Bollobás theorem is valid.
Banach J. Math. Anal., Volume 10, Number 3 (2016), 621-637.
Received: 19 November 2015
Accepted: 28 November 2015
First available in Project Euclid: 22 August 2016
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 46B04: Isometric theory of Banach spaces
Secondary: 46B20: Geometry and structure of normed linear spaces 46B22: Radon-Nikodým, Kreĭn-Milman and related properties [See also 46G10] 47A30: Norms (inequalities, more than one norm, etc.)
Kadets, Vladimir; Martín, Miguel; Soloviova, Mariia. Norm-attaining Lipschitz functionals. Banach J. Math. Anal. 10 (2016), no. 3, 621--637. doi:10.1215/17358787-3639646. https://projecteuclid.org/euclid.bjma/1471873728