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.

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  • 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.
Opuscula Mathematica - cover

Cite this article as:
Ewa Szlachtowska, Dominik Mielczarek, On the uniqueness of minimal projections in Banach spaces, Opuscula Math. 32, no. 3 (2012), 579-590, http://dx.doi.org/10.7494/OpMath.2012.32.3.579

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