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- W2007653296 abstract "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 (min0,max0)-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 (min0,max0)-nuclear if and only if A is a nuclear C∗-algebra." @default.
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- W2007653296 date "2012-12-01" @default.
- W2007653296 modified "2023-09-26" @default.
- W2007653296 title "Tensor products for non-unital operator systems" @default.
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- W2007653296 doi "https://doi.org/10.1016/j.jmaa.2012.07.011" @default.
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