A survey of noncommutative dynamical entropy

The paper is a survey of dynamical entropy of automorphisms of operator algebras. We describe the different entropies of Connes-Stormer, Connes-Narnhofer-Thirring, Sauvageot-Thouvenot, and Voiculescu, and discuss the main examples of the theory.Comment: 48 pages, late

A reduction theorem for capacity of positive maps

We prove a reduction theorem for capacity of positive maps of finite dimensional C*-algebras, thus reducing the computation of capacity to the case when the image of a nonscalar projection is never a projection.Comment: 7 page

Separable states and the SPA of a positive map

We introduce a nessecary condition for a state to be separable and apply this condition to the SPA of an optimal ositive map and give a proof of the fact that the SPA need not be the density ooperator for a separable state

Multiplicative properties of positive maps

Let $\phi$ be a positive unital normal map of a von Neumann algebra $M$ into itself, and assume there is a family of normal $\phi$-invariant states which is faithful on the von Neumann algebra generated by the image of $\phi$. It is shown that there exists a largest Jordan subalgebra $C_\phi$ of $M$ such that the restriction of $\phi$ to $C_\phi$ is a Jordan automorphhism, and each weak limit point of $(\phi^n (a))$ for $a\in M$ belongs to $C_\phi$.Comment: 8 page

A Christmas hymn by Martin Luther

From heaven above\u27