2012/06/30 by Volker Thürey, Volker Wilhelm Thürey, Thürey, Volker Wilhelm
Computer Science · Engineering · Mathematics · #2010: 46B20 #52A10 #Advanced Numerical Analysis Techniques #Advanced Theoretical and Applied Studies in Material Sciences and Geometry #FOS: Mathematics #Functional Analysis (math.FA) #Optimization and Variational Analysis #math.FA #msc:46B20 #msc:52A10
paper · pdf · doi:10.48550/arxiv.1207.0074
23 pages, 1 figure
arxiv created 2012/06/30 · openalex publication_date 2012/06/30 · arxiv updated 2012/07/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
We suggest a concept of generalized `angles' in arbitrary real normed vector spaces. We give for each real number a definition of an `angle' by means of the shape of the unit ball. They all yield the well known Euclidean angle in the special case of real inner product spaces. With these different angles we achieve a classification of normed spaces, and we obtain a characterization of inner product spaces. Finally we consider this construction also for a generalization of normed spaces, i.e. for spaces which may have a non-convex unit ball.