Opuscula Math. 32, no. 3 (2012), 579-590
http://dx.doi.org/10.7494/OpMath.2012.32.3.579
Opuscula Mathematica
On the uniqueness of minimal projections in Banach spaces
Ewa Szlachtowska
Dominik Mielczarek
Abstract. Let \(X\) be a uniformly convex Banach space with a continuous semi-inner product. We investigate the relation of orthogonality in \(X\) and generalized projections acting on \(X\). We prove uniqueness of orthogonal and co-orthogonal projections.
Keywords: minimal projection, orthogonal projection, co-orthogonal projection, uniqueness of norm-one projection.
Mathematics Subject Classification: 41A65, 46B20, 46B25.
- Ewa Szlachtowska
- AGH University of Science and Technology, Faculty of Applied Mathematics, al. Mickiewicza 30, 30-059 Krakow, Poland
- Dominik Mielczarek
- AGH University of Science and Technology, Faculty of Applied Mathematics, al. Mickiewicza 30, 30-059 Krakow, Poland
- Received: 2012-02-19.
- Revised: 2012-03-18.
- Accepted: 2012-03-20.
