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The ultimate estimate of the upper norm bound for the summation of operators |
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| Authors: | Man-Duen Choi Chi-Kwong Li |
| Institution: | a Department of Mathematics, University of Toronto, Toronto, Ont., Canada M5S 2E4 b Department of Mathematics, College of William & Mary, Williamsburg, VA 23187-8795, USA |
| Abstract: | Let A and B be bounded linear operators acting on a Hilbert space H. It is shown that the triangular inequality serves as the ultimate estimate of the upper norm bound for the sum of two operators in the sense that sup{∥U*AU+V*BV∥:U and V are unitaries}=min{∥A+μI∥+∥B-μI∥:μ∈C}. |
| Keywords: | 47A30 47A12 15A60 |
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