Geodesic
The Representation Theorem for Local Operator Spaces
Funkcionalʹnyj analiz i ego priloženiâ, Tome 41 (2007) no. 4, pp. 73-78.

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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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A. A. Dosiev. The Representation Theorem for Local Operator Spaces. Funkcionalʹnyj analiz i ego priloženiâ, Tome 41 (2007) no. 4, pp. 73-78. http://geodesic.mathdoc.fr/item/FAA_2007_41_4_a6/

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