Characterizations of Norm–Parallelism in Spaces of Continuous Functions

  • Ali Zamani
Original Paper


In this paper, we consider the characterization of norm–parallelism problem in some classical Banach spaces. In particular, for two continuous functions fg on a compact Hausdorff space K, we show that f is norm–parallel to g if and only if there exists a probability measure (i.e., positive and of full measure equal to 1) \(\mu \) with its support contained in the norm-attaining set \(\{x\in K: \, |f(x)| = \Vert f\Vert \}\) such that \(\big |\int _K \overline{f(x)}g(x){\text {d}}\mu (x)\big | = \Vert f\Vert \,\Vert g\Vert \).


Norm–parallelism Banach space of continuous functions Probability measure 

Mathematics Subject Classification

47A30 46B20 46E15 



The author would like to thank the referees for their careful reading of the manuscript and useful comments.


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Copyright information

© Iranian Mathematical Society 2018

Authors and Affiliations

  1. 1.Department of MathematicsFarhangian UniversityTehranIran

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