A note on the minimal tensor product and the C*-envelope of operator systems

Abstract

In this article, we show that the $C^*$-envelope of the minimal tensor product of two operator systems is isomorphic to the minimal tensor product of their $C^*$-envelopes. We do this by identifying the Silov boundary ideal of the minimal tensor product of two operator systems. Finally, as an application of this result, we show that the propagation number of the minimal tensor product of operator systems is the maximum of the propagation numbers of the factors.