Book Chapter10.1007/978-3-0348-9076-2_5
Matrix Young Inequalities
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TL;DR: In this paper, it was shown that for any pair A, B of n × n complex matrices there is a unitary matrix U, depending on A and B, such that p, q > 0 satisfy 1/p + 1/q = 1.
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Abstract: Let p, q > 0 satisfy 1/p + 1/q = 1. We prove that for any pair A, B of n × n complex matrices there is a unitary matrix U, depending on A, B, such that
$$U*\left| {AB*} \right|U \leqslant {\left| A \right|^p}/p + {\left| B \right|^q}/q.$$
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References
On the singular values of a product of operators
Rajendra Bhatia,Fuad Kittaneh +1 more
TL;DR: For compact Hilbert space operators A and B, the singular values of B and A were shown to be dominated by the singular value of 1/2/1/2 (AA + BB + BB ) as mentioned in this paper.
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