Angles in normed spaces

V. Balestro, Á. G. Horváth, H. Martini and R. Teixeira, Angles in normed spaces, Aequationes Mathematicae 91(2), pp. 201-236, 2017. (arXiv link) (journal link)

Comments: It is well known that there is no “completely natural” definition of angle measures for an arbitrary normed space. Just like in the case of orthogonality concepts, several angle concepts can be defined, each of them carrying some properties of the usual Euclidean angle. This work is an expository paper that originally aimed to gather together the angle concepts that have already appeared in the literature. We emphasize the cases where the angle concepts preserve orthogonality types, and survey also angle concepts given by Borel measures in the unit circle. A new angle function related to the Minkowski sine function is also given.