Decompositions of operator-valued representations of function algebras

W. Mlak

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The Stinespring theorem is reformulated in terms of conditional expectations in a von Neumann algebra. A generalisation for map-valued measures is obtained.

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Measures connected with Bargmann's representation of the q-commutation relation for q > 1

Ilona Królak (1998)

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Classical Bargmann’s representation is given by operators acting on the space of holomorphic functions with scalar product $〈 z^{n}, z^{k} 〉_{q} = δ_{n, k} {[n]}_{q}! = F (z^{n} {\bar{z}}^{k})$ . We consider the problem of representing the functional F as a measure. We prove the existence of such a measure for q > 1 and investigate some of its properties like uniqueness and radiality.