Tensor products for non-unital operator systems

[摘要] In this short article, we study tensor products of not necessarily unital operator systems (for short, NUOS). We will define canonical functorial NUOS tensor products (in a similar fashion to Kavruk et al. (2011) [4]) as well as a subclass of them consisting of reduced functorial NUOS tensor products (that are defined through a unitalization process). We show that if a NUOS X is (Min, Max)-nuclear (in the sense that there is only one NUOS tensor product of X with any NUOS Y), then X is trivial. However, if V is a unital operator system, then V is (min(0), max(0))-nuclear (in the sense that there is only one reduced NUOS tensor product of V with any NUOS Y) if and only if V is (min, max)-nuclear in the sense of Han and Paulsen (2011)[2] (i.e. there is only one unital operator system tensor product of V with any unital operator system W). On the other hand, a C*-algebra A is (min(0), max(0))-nuclear if and only if A is a nuclear C*-algebra. (C) 2012 Elsevier Inc. All rights reserved.

[发布日期] 2012-12-15

[关键词] Non-unital operator systems;Tensor products