On analytic factorization of positive hermitian matrix functions over the bidisc

Let Omega:T-2 --> M-N(C) be a positive hermitian (Omega greater than or equ al to 0) matrix-valued function on the bitorus with integral integral(T2) l og det Omega > -infinity and integral integral(T2) parallel to Omega parall el to < infinity. Then Omega is the L-1-limit of FjFj*, where F-j is a (N x N-j) rectangular bi-analytic matrix function. A continuous and strictly po sitive hermitian Omega:T-2 --> M-N may be factored as FF* with F an N x inf inity analytic operator function. (C) 1999 Elsevier Science Inc. All rights reserved.