Multilinear maps on products of operator algebras |
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Authors: | JDMaitland Wright Kari Ylinen |
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Institution: | a Mathematics Department, University of Reading, Reading RG6 6AX, England, UK b Department of Mathematics, University of Turku, FIN-20014 Turku, Finland |
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Abstract: | Let A1,A2,…,Ar be C∗-algebras with second duals A1″,A2″,…,Ar″, and let X be an arbitrary Banach space. Let be a bounded r-linear map, and denote by the Johnson-Kadison-Ringrose extension (i.e., the separately to continuous r-linear extension) of Γ. The problem of characterising those Γ for which Γ″ takes its values in X was solved by Villanueva when the algebras are all commutative. Because the Dunford-Pettis property fails for noncommutative C∗-algebras, the ‘obvious’ extension of Villanueva's characterisation does not give the correct condition. In this paper we solve this problem for general C∗-algebras. This result is then applied to obtaining a multilinear generalisation of the normal-singular decomposition of a bounded linear operator on a von Neumann algebra. |
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