Abstract
The definition of a completely positive invariant multilinear map from aC*-algebra to another is introduced. We construct the representation of a completely positive invariant multilinear map on a HilbertC*-module without the bridging maps. This is another extension of the Stinespring’s representation, which is different from a multilinear representation of Christensen and Sinclair. We give the covariant representation of completely positive invariant covariant multilinear maps on a HilbertC*-module. Further, we investigate the order structure of such maps and obtain a generalization of the Radon-Nikodym theorem.
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Heo, J. Representations of invariant multilinear maps on HilbertC*-modules. Isr. J. Math. 118, 125–146 (2000). https://doi.org/10.1007/BF02803519
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DOI: https://doi.org/10.1007/BF02803519