On factorization of biinfinite totally positive block toeplitz matrices

We extend the work of Aissen, Schoenberg, Whitney, and Edrei, who characterized the symbol of a totally positive Toe- plitz matrix, to characterizing the determinant of the symbol of a block Toeplitz totally positive matrix. As a consequence of our arguments we show that the symbol for the block Toeplitz case may be factored just as in the Toeplitz setting. © 1986 Rocky Mountain Mathematics Consortium.