Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 44, 2019, 769-789

MAPPINGS PRESERVING SEGAL'S ENTROPY IN VON NEUMANN ALGEBRAS

Andrzej Luczak and Hanna Podsędkowska

Lódz University, Faculty of Mathematics and Computer Science
ul. S. Banacha 22, 90-238 Lódz, Poland; andrzej.luczak 'at' wmii.uni.lodz.pl

Lódz University, Faculty of Mathematics and Computer Science
ul. S. Banacha 22, 90-238 Lódz, Poland; hanna.podsedkowska 'at' wmii.uni.lodz.pl

Abstract. We investigate the situation when a normal positive linear unital map on a semifinite von Neumann algebra leaving the trace invariant does not change the Segal entropy of the density of a normal, not necessarily normalised, state. Two cases are dealt with: a) no restriction on the map is imposed, b) the map represents a repeatable instrument in measurement theory which means that it is idempotent.

2010 Mathematics Subject Classification: Primary 46L53; Secondary 81P45.

Key words: Segal entropy, semifinite von Neumann algebra, positive maps.

Reference to this article: A. Luczak and H. Podsędkowska: Mappings preserving Segal's entropy in von Neumann algebras. Ann. Acad. Sci. Fenn. Math. 44 (2019), 769-789.

Full document as PDF file

https://doi.org/10.5186/aasfm.2019.4439