Every operator space has an injective envelope, obtained as the range of a minimal idempotent in the compact semigroup of completely contractive self-maps fixing the space.
Conway,A course in functional analysis, 2nd ed., Graduate Texts in Mathematics, vol
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A short proof of the existence of the injective envelope of an operator space
Every operator space has an injective envelope, obtained as the range of a minimal idempotent in the compact semigroup of completely contractive self-maps fixing the space.