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Mappings preserving quantum Renyi's entropies in von Neumann algebras
Andrzej Łuczak, Hanna Podsędkowska, Rafał Wieczorek
We investigate the situation when a normal positive linear unital map on a semifinite von Neumann algebra leaving the trace invariant does not change fixed quantum Renyi's entropy…
Relative modular operator in semifinite von Neumann algebras and its use
Andrzej Łuczak, Hanna Podsędkowska, Rafał Wieczorek
We present some results concerning the relative modular operator in semifinite von Neumann algebras. These results allow one to prove some basic formula for trace, to obtain equiva…
The eigenvectors of semigroups of positive maps on von Neumann algebras
Andrzej Łuczak
The eigenvectors of an ergodic semigroup of linear normal positive unital maps on a von Neumann algebra are described. Moreover, it is shown by means of examples, that mere positiv…
Quantum stochatic integrals and Doob-Meyer decomposition
Andrzej Luczak
We show that for a quantum -martingale , , there exists a Doob-Meyer decomposition of the submartingale . A noncommutative counterpart of a classical…
Frobenius theory fails for semigroups of positive maps on von Neumann algebras
Andrzej Luczak
The eigenvectors of an ergodic semigroup of linear normal positive unital maps on a von Neumann algebra are described. Moreover, it is shown by means of examples, that mere positiv…
Structure of the time projection for stopping times in von Neumann algebras
Andrzej Luczak
We give an explicit formula for the time projection in an arbitrary von Neumann algebra from which all its basic properties can be easily derived. The analysis of the situation whe…