Quantum limit theorems
Tom 164 / 2004
Studia Mathematica 164 (2004), 103-120 MSC: Primary 46L53; Secondary 60F05. DOI: 10.4064/sm164-2-1
A noncommutative analogue of limit theorems in classical probability theory for distributions of canonical pairs of observables is considered. A complete description of all limit probability operators which are quantum counterparts of the classical infinitely divisible and semistable laws is obtained in the case when scalar norming is generalised to norming by $2\times 2$ matrices.