Abstract:
In this note we propose a representation theorem for local operator spaces which extends Ruan's representation theorem for operator spaces, and Arveson–Hahn–Banach–Webster theorem for local operator systems. Further, we investigate the decomposition property of a complete contraction from a unital multinormed $C^*$-algebra into a local operator system as a product of contractions and unital contractive $*$-representation, and the injectivity in both local operator space and local operator system contexts.
Keywords:local operator space, local operator system, multinormed $C^*$-algebra.
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