Factoring non-negative operator valued trigonometric polynomials in two variables

Abstract

AbstractIt is shown using Schur complement techniques that on finite dimensional Hilbert spaces, a non-negative operator valued trigonometric polynomial in two variables with degree $$(d_1,d_2)$$ ( d 1 , d 2 ) can be written as a sum of hermitian squares of at most $$2d_2$$ 2 d 2 analytic polynomials.