Abstract
In this note, we generalize Ruan’s representation theorem and propose an Arveson-Hanh-Banach-Webster theorem for local operator spaces. Further, we investigate the decompos-ability of a complete contraction acting from a unital multinormed C*-algebra to a local operator System into a product of contractions and a unital contractive *-representation, and we study injectivity in both local operator space and local operator System contexts.
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Translated from Funktsional’nyi Analiz i Ego Prilozheniya, Vol. 41, No. 4, pp. 73–78, 2007
Original Russian Text Copyright © by A. Dosiev
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Dosiev, A. A representation theorem for local operator spaces. Funct Anal Its Appl 41, 306–310 (2007). https://doi.org/10.1007/s10688-007-0029-4
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DOI: https://doi.org/10.1007/s10688-007-0029-4