Aequat. Math. c Springer International Publishing AG, part of Springer Nature 2018 Aequationes Mathematicae https://doi.org/10.1007/s00010-018-0571-6 S. M. S. Nabavi Sales Abstract. In this paper, we study mappings, which approximately preserve angles between inner product spaces. We also introduce a notion of angle in normed spaces. The notion of angle, considered in this part, relates to the well-known Birkhoﬀ–James orthogonality. Based on it, we express a characterization for approximate Birkhoﬀ–James orthogonality, introduced in the literature, through this notion of angle. Then we return to the issue of mappings which approximately preserve angle stating some results in normed spaces. Mathematics Subject Classiﬁcation. 47B49, 46C05, 46B20. Keywords. Angle in normed spaces, Birkhoﬀ–James orthogonality, Approximate orthogonal- ity preserving, Approximate angle preserving. 1. Introduction In this paper, we deal with mappings which approximately preserve angles. This issue arises, originally, from investigations on complex functions. A com- plex function that preserves angles and distances against any extreme defor- mation, is likely to preserve many geometric aspects, approximately. In a real inner product space (X , ., .), the angle between two non-zero vectors x and y is deﬁned, routinely, by invoking the inner product. Indeed x∠ y for some x,y θ ∈ [0,π] if and
aequationes mathematicae – Springer Journals
Published: May 30, 2018
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