DYNAMICS ON NONCOMMUTATIVE ORLICZ SPACES

• 作者: L.E.LABUSCHAGNE W.A.MAJEWSKI
• 来源期刊: 数学物理学报（英文版）
• 年，卷（期）: 2020,（5）
• 页码范围: 1249-1270
• 页数: 22页
• 语种: 英文

摘要

Quantum dynamical maps are defined and studied for quantum statistical physics based on Orlicz spaces.This complements earlier work[26]where we made a strong case for the assertion that statistical physics of regular systems should properly be based on the pair of Orlicz spaces <Lcosh-1,L log(L + 1)>,since this framework gives a better description of regular observables,and also allows for a well-defined entropy function.In the present paper we "complete" the picture by addressing the issue of the dynamics of such a system,as described by a Markov semigroup corresponding to some Dirichlet form (see[4,13,14]).Specifically,we show that even in the most general non-commutative contexts,completely positive Markov maps satisfying a natural Detailed Balance condition canonically admit an action on a large class of quantum Orlicz spaces.This is achieved by the development of a new interpolation strategy for extending the action of such maps to the appropriate intermediate spaces of the pair <L∞,L1>.As a consequence,we obtain that completely positive quantum Markov dynamics naturally extends to the context proposed in[26].