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1
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A survey of certain trace inequalities

100%
Petz D.
Banach Center Publications
|
1994
|
tom 30
|
nr 1
287-298
EN
This paper concerns inequalities like TrA ≤ TrB, where A and B are certain Hermitian complex matrices and Tr stands for the trace. In most cases A and B will be exponential or logarithmic expressions of some other matrices. Due to the interest of the author in quantum statistical mechanics, the possible applications of the trace inequalities will be commented from time to time. Several inequalities treated below have been established in the context of Hilbert space operators or operator algebras. Notwithstanding these extensions our discussion will be limited to matrices.
2
Content available remote

A new approach to mutual information

63%
Hiai F., Petz D.
Banach Center Publications
|
2007
|
tom 78
|
nr 1
151-164
EN
A new expression as a certain asymptotic limit via "discrete micro-states" of permutations is provided for the mutual information of both continuous and discrete random variables.
3
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A free analogue of the transportation cost inequality on the circle

63%
Hiai F., Petz D.
Banach Center Publications
|
2006
|
tom 73
|
nr 1
199-206
4
Content available remote

Chain rules for canonical state extensions on von Neumann algebras

63%
Cecchini C., Petz D.
Colloquium Mathematicum
|
1993
|
tom 64
|
nr 1
115-119
EN
In previous papers we introduced and studied the extension of a state defined on a von Neumann subalgebra to the whole of the von Neumann algebra with respect to a given state. This was done by using the standard form of von Neumann algebras. In the case of the existence of a norm one projection from the algebra to the subalgebra preserving the given state our construction is simply equivalent to taking the composition with the norm one projection. In this paper we study couples of von Neumann subalgebras in connection with the state extension. We establish some results on the ω-conditional expectation and give a necessary and sufficient condition for the chain rule of our state extension to be true.
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