Minimal Stinespring Representations of Operator Valued Multilinear Maps

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A completely positive linear map φ from a C*-algebra A into B(H) has a Stinespring representation as φ(a) = X*π(a)X, where π is a *- representation of A on a Hilbert space K and X is a bounded operator from H to K. Completely bounded multilinear operators on C*-algebras as well as some densely defined multilinear operators in Connes’ noncommutative geometry also have Stinespring representations of the form (Formula Presented) such that each ai is in a *-algebra Ai and X0,…, Xk are densely defined closed operators between the Hilbert spaces. We show that for both completely bounded maps and for the geometrical maps, a natural minimality assumption implies that two such Stinespring representations have unitarily equivalent *-representations in their decompositions.

TidsskriftJournal of Operator Theory
Udgave nummer2
Sider (fra-til)587-601
Antal sider15
StatusUdgivet - 2023

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