Angles and Polar Coordinates In Real Normed Spaces

We try to create a wise definition of ‘angle spaces’. Based on an idea of Ivan Singer, we introduce a new concept of an angle in real Banach spaces, which generalizes the euclidean angle in Hilbert spaces. With this angle it is shown that in every two-dimensional subspace of a real Banach space we can describe elements uniquely by polar coordinates.

💡 Research Summary

The paper tackles the long‑standing problem of defining a meaningful notion of angle in real Banach spaces, where no inner product is available. Building on an idea originally suggested by Ivan Singer, the authors introduce a norm‑based angle between two non‑zero vectors (x) and (y) by the formula
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