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A Birkhoff-James cosine function for normed linear spaces

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Abstract

The cosine function is a classical tool for measuring angles in inner product spaces, and it has various extensions to normed linear spaces. In this paper, we investigate a cosine function for the convex angle formed by two nonzero elements of a complex normed linear space, in connection with recent results on the Birkhoff-James approximate orthogonality sets.

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Notes

  1. For notational convenience, in this article, we consider the set \(F_{\varepsilon }(\psi ;\chi )\) instead of \(F_{\varepsilon }(\chi ;\psi )\) which was introduced and studied in [18, 23].

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Correspondence to Panayiotis Psarrakos.

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Panagakou, V., Psarrakos, P. & Yannakakis, N. A Birkhoff-James cosine function for normed linear spaces. Aequat. Math. 95, 889–914 (2021). https://doi.org/10.1007/s00010-021-00791-0

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