Trigonometry on the Unit Ball of a Complex Hilbert Space
نویسنده
چکیده
1. Introduction. The unit disc furnished with the Poincaré metric provides a model (the Poincaré model) for the hyperbolic geometry. The linear fractional transformations of the unit disc onto itself constitute the group of motions. An analogous phenomenon arises in the unit ball of any complex Hubert space when it is furnished with the Carathéodory-Reiffen metric. The purpose of this note is to announce the hyperbolic version of the laws of sines and cosines, and the Pythagorean theorem on the unit ball of any complex Hubert space.
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تاریخ انتشار 2007