Some trace inequalities for exponential and logarithmic functions
Consider a function F(X,Y ) of pairs of positive matrices with values in the positive matrices such that whenever X and Y commute F(X,Y ) = XpYq. Our first main result gives conditions on F such that Tr[X log(F(Z,Y ))] ≤Tr[X(p log X + q log Y )] for all X,Y,Z such that TrZ = TrX. (Note that Z is abs...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
World Scientific Publishing
2019-08-01
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| Series: | Bulletin of Mathematical Sciences |
| Subjects: | |
| Online Access: | http://www.worldscientific.com/doi/pdf/10.1142/S1664360719500085 |