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Aix-Marseille Université
Institut de Mathématiques de Marseille (I2M) - UMR 7373
Site Saint-Charles : 3 place Victor Hugo, Case 19, 13331 Marseille Cedex 3
Site Luminy : Campus de Luminy - Case 907 - 13288 Marseille Cedex 9

Séminaire

Commutativity of operator tuples

Kehe Zhu
Department of Mathematics and Statistics, State University of New York at Albany
https://www.albany.edu/~kzhu/english.html

Date(s) : 11/12/2014   iCal
11h00 - 12h00

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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