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There are two basic angles associated with a pair of linear subspaces: theDiximier angle and the Friedrichs angle. The Dixmier angle of the pair oforthogonal complements is the same as the Dixmier angle of the original pairprovided that the original pair gives rise to a direct (not necessarilyorthogonal) sum of the underlying Hilbert space. The Friedrichs angles of theoriginal pair and the pair of the orthogonal complements always coincide. Thesetwo results are due to Krein, Krasnoselskii, and Milman and to Solmon,respectively. In 1995, Deutsch provided a very nice survey with complete proofsand interesting historical comments. One key result in Deutsch's survey was aninequality for Dixmier angles provided by Hundal.  In this paper, we present extensions of these results to the case when thelinear subspaces are only required to be convex cones. It turns out thatHundal's result has a nice conical extension while the situation is moretechnical for the results by Krein et al.\ and by Solmon. Our analysis is basedon Deutsch's survey and our recent work on angles between convex sets.Throughout, we also provide examples illustrating the sharpness of our results.

On angles between convex cones