Matrix Order in Bohr Inequality for Operators
نویسندگان
چکیده
The classical Bohr inequality says that |a+b| ≤ p|a|+q|b| for all scalars a, b and p, q > 0 with 1 p + 1 q = 1. The equality holds if and only if (p− 1)a = b. Several authors discussed operator version of Bohr inequality. In this paper, we give a unified proof to operator generalizations of Bohr inequality. One viewpoint of ours is a matrix inequality, and the other is a generalized parallelogram law for absolute value of operators, i.e., for operators A and B on a Hilbert space and t 6= 0, |A−B| + 1 t |tA + B| = (1 + t)|A| + (1 + 1 t )|B|.
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