Factoring non-negative operator valued trigonometric polynomials in two variables

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2024年6月27日

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Michael A. Dritschel

摘要

It 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.