On certain properties of the relative entropy of states of operator algebras.
A survey of certain trace inequalities
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....
Compactness as -pseudocompactness
Chain rules for canonical state extensions on von Neumann algebras
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...
A large deviation theorem for the empirical eigenvalue distribution of random unitary matrices
A free analogue of the transportation cost inequality on the circle
A new approach to mutual information
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.
Means of positive matrices: geometry and a conjecture.
On the function .
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