For finite dimentional inner product spaces, the concept of angle between two vectors is widely used in geometry and in physics. Are there any applications of this concept in infinite dimensional spaces? (Other than angles of $0$ and $\frac \pi 2$ implying linear dependence and orthogonality, of course)
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$\begingroup$ Countable unions of sets in a Banach space that are nowhere dense in a certain strong way, namely at each point in the set there is a cone with some angular aperture size whose interior has empty intersection with the set (see this google search), are used to strengthen first Baire category exceptional set results involving the differentiability of Lipschitz functions defined on a Banach space -- see this google search. $\endgroup$– Dave L. RenfroCommented Jan 28, 2023 at 18:16
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Friedrich's angle is something that comes to mind. It is a generalisation of the angle between one dimensional subspaces.
It is used e.g. in this (rather fascinating paper):
The rate of convergence in the method of alternating projections
answered Feb 10, 2023 at 9:59