NONSURJECTIVE MAPS BETWEEN RECTANGULAR MATRIX SPACES PRESERVING DISJOINTNESS, TRIPLE PRODUCTS, OR NORMS

摘要

Let M-m,M-n be the space of m x n real or complex rectangular matrices. Two matrices A, B is an element of M-m,M-n are disjoint if A * B = 0(n) and AB* = 0(m). We show that a linear map Phi : M-m,M-n -> M-r,M-s preserving disjointness exactly when Phi(A) = u (A circle times Q(1) 0 0 0 A(t)circle times Q(2) 0 0 0) V, for all A is an element of M-m,M-n for some unitary matrices U is an element of M-r,M-r and V is an element of M-s,M-s, and positive diagonal matrices Q(1), Q(2), where Q(1) or Q(2) may be vacuous. The result is used to characterize nonsurjective linear maps between rectangular matrix spaces preserving (zero) JB*-triple products, the Schatten p-norms or the Ky-Fan k-norms.

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