A Characterization of the Operator-valued Triangle Equality
نویسندگان
چکیده
We will show that for any two bounded linear operators X, Y on a Hilbert space H, if they satisfy the triangle equality |X + Y | = |X | + |Y |, there exists a partial isometry U on H such that X = U |X | and Y = U |Y |. This is a generalization of Thompson’s theorem to the matrix case proved by using a trace. 47A05, 47A10, 47A12 operator theory, Hilbert space, triangle inequality
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