On Geometry of Banach Function Modules: Selected Topics

Paweł Wójcik ()
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Paweł Wójcik: Pedagogical University of Cracow, Department of Mathematics

Chapter Chapter 20 in Ulam Type Stability, 2019, pp 453-468 from Springer

Abstract: 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 C ( K ; X ) $$\mathcal {C}(K;X)$$ , and to give a new characterization of smooth points in C ( K ) $$\mathcal {C}(K)$$ . 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; Primary 46B20, 39B82; Secondary 46E15, 39B52, 46C50 (search for similar items in EconPapers)
Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-030-28972-0_20

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DOI: 10.1007/978-3-030-28972-0_20

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