Real Structure in Operator Spaces, Injective Envelopes and G-spaces

We present some more foundations for a theory of real structure in operator spaces and algebras, in particular concerning the real case of the theory of injectivity, and the injective, ternary, and \(C^*\) $C^{\ast }$ -envelope. We consider the interaction between these topics and the complexification. We also generalize many of these results to the setting of operator spaces and systems acted upon by a group.