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.

Full text (pdf)

• 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
• Revised: 2012-03-18.
• Accepted: 2012-03-20.