I'm looking for examples of (max-min)-nuclear operator systems.
In one of the papers that I'm reading, an operator system is said to be nuclear provided that the minimal tensor product of it with an arbitrary operator system. This property is also known as (max-min)-nuclear.
Let $\mathcal{S}$ be an operator system. Then we say that $\mathcal{S}$ is (max-min)-nuclear if, for any operator system $\mathcal{T}$ it holds $$\mathcal{S}\otimes_{max}\mathcal{T}=\mathcal{S}\otimes_{min}\mathcal{T}.$$
I found only an example for the moment:
Let $\mathcal{K}_0 \subset \mathcal{B}(l^2(\mathbb{N}))$ denote the norm closed linear span of $\{E_{i,j}: (i,j) \neq (1,1)\}$, where $E_{i,j}$ are the standard matrix units and let $$\mathcal{S}_0 = \{\lambda I +K_0: \lambda \in \mathbb{C}, K_0 \in \mathcal{K}_0 \}$$
denote the operator system spanned by $\mathcal{K}_0$ and the identity operator. It is proven that $\mathcal{S}_0$ is a nuclear operator system that is no unitally completely order isomorphic to any $C^*$-algebra.
Does anyone know other examples?
I'm looking for examples of "self"-nuclear operator systems, i.e., operator system for which the equality given before holds just between $\mathcal{S}$ and itself.
Are there any such examples?
Thanks in advance,
Francesca