The Finsler geometry of certain covering groups of operator groups
In J. Aust. Math. Soc. 42, 196-222 (1987; Zbl 0614.58007), the author has investigated the Finsler geometry - in a natural Finsler structure - of both the full and the Fredholm unitary, orthogonal, and symplectic groups of a Hilbert space. In this sequel he considers similar questions for the associated non-trivial covering groups, namely the Fredholm spinor group and the coverings of the Fredholm unitary group. There is no evident relation between the global Finsler geometry of a covering group and that of the original group, unless one remains sufficiently close to the identity, and the author presents some unexpected results, e.g. that the universal cover of the Fredholm unitary group is bounded if and only if the underlying Hilbert space is of infinite dimension.
scientific article; zbMATH DE number 4104021