Operator versions of Shannon type inequality

Cyclic Refinements of the Different Versions of Operator Jensen's Inequality

A non-Shannon-type conditional inequality of information quantities

Given n discrete random variables = fX1; ; Xng, associated with any subset of f1; 2; ; ng, there is a joint entropy H(X ) where X = fXi: i 2 g. This can be viewed as a function defined on 2 2; ; ng taking values in [0; +1). We call this function the entropy function of . The nonnegativity of the joint entropies implies that this function is nonnegative; the nonnegativity of the conditional join...

A Note on Matrix Versions of Kantorovich–type Inequality

Some new matrix versions of Kantorovich-Type inequalities for Hermitian matrix are proposed in this paper. We consider what happens to these inequalities when the positive definite matrix is allowed to be positive semidefinite singular or indefinite.

On a New Non-shannon Type Information Inequality∗

Recently, K. Makarychev, Y. Makarychev, A. Romashchenko and N. Vereshchagin proved a new non-Shannon-type information inequality [3] involving 5 random variables which can be viewed as a natural generalization of the ZY98 inequality. In this article, we give a simple proof of a further generalized version of this new inequality and explain its information theoretical meaning by formulating two ...

An Operator Extension of Bohr's inequality