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On Geometry of Banach Function Modules: Selected Topics

  • Paweł WójcikEmail author
Chapter

Abstract

The aim of the paper is to present results concerning the geometry of Banach function modules. In particular, we characterize the k-smooth points in Banach function modules and we compute the norm derivatives in Banach function modules. Using the notion of the norm derivatives, we apply our results to characterize orthogonality in the sense of Birkhoff in \(\mathcal {C}(K;X)\), and to give a new characterization of smooth points in \(\mathcal {C}(K)\). Moreover, the stability of the orthogonality equation in normed spaces is considered.

Keywords

Function module Extreme point k-Smooth point Norm derivatives Stability Orthogonality equation 

Mathematics Subject Classification (2010)

Primary 46B20 39B82; Secondary 46E15 39B52 46C50 

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of MathematicsPedagogical University of CracowKrakówPoland

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