Abstract
Let C*(F∞) be the full C*-algebra associated to the free group of countably many generators and SnC*(F∞) be the class of all n-dimensional operator subspaces of C*(F∞). In this paper, we study some stability properties of SnC*(F∞). More precisely, we will prove that for any E0, E1 in SnC*(F∞), the Haagerup tensor product E0⊗hE1 and the operator space obtained by complex interpolation Eθ are (1 + ∈)-contained in C*(F∞) for arbitrary ∈>0. On the other hand, we will show an extension property for WEPC*-algebras.
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