Commutativity of operator tuples

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Date(s) - 11/12/2014
11 h 00 min - 12 h 00 min

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Suppose A = (A1,…,An) is a tuple of N × N normal matrices. We show that the matrices in the tuple pairwise commute if and only if the polynomial p(z1,…,zn) = det(I + z1A1 + … + znAn) is completely reducible, namely, it can be factored into a product of linear polynomials. We will also generalize the result to the case of self-adjoint compact operators on a Hilbert space.


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