Abstract
Let A kbe the group of isometries of the space of n-by-n matrices over reals (resp. complexes, quaternions) with respect to the Ky Fan k-norm (see the Introduction for the definitions). Let Γ0 be the group of transformations of this space consisting of all products of left and right multiplications by the elements of SO(n)(resp. U(n), Sp(n)). It is shown that, except for three particular casesAk coincides with the normalizer of Γ in Δ group of isometries of the above matrix space with respect to the standard inner product. We also give an alternative treatment of the case D = R n = 4k = 2 which was studied in detail by Johnson, Laffey, and Li [4].
*This work was supported by the NSERC of Canada Grant A-5285
*This work was supported by the NSERC of Canada Grant A-5285
Notes
*This work was supported by the NSERC of Canada Grant A-5285