Normal approximants to binormal operators

Bhatia, Rajendra ; Horn, Roger A. ; Kittaneh, Fuad (1991) Normal approximants to binormal operators Linear Algebra and its Applications, 147 . pp. 169-179. ISSN 0024-3795

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Let T=[Tij], i,j=1,2,…,m, be a block operator whose entries Tij are commuting normal operators on a Hilbert space. We give a simple proof of the known fact that such operators can be reduced to an upper triangular form via a unitary conjugation. Our proof brings out some useful features of the triangular form. When m=2 we find the closest normal operator to the binormal operator T with respect to every unitarily invariant norm. This is a generalization of a result of J. Phillips, who solved this approximation problem for the operator bound norm.

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