Dilations,Product Systems,and Weak Dilations |
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Authors: | Skeide M |
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Institution: | (1) Brandenburgische Technische Universität, Cottbus, Germany |
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Abstract: | We generalize Bhat's construction of product systems of Hilbert spaces from E0-semigroups on B(H) for some Hilbert space H to the construction of product systems of Hilbert modules from E0-semigroups on Ba(E) for some Hilbert module E. As a byproduct we find the representation theory for Ba(E) if E has a unit vector. We establish a necessary and sufficient criterion for the conditional expectation generated by the unit vector to define a weak dilation of a CP-semigroup in the sense of 1]. Finally, we also show that white noises on general von Neumann algebras in the sense of 2] can be extended to white noises on a Hilbert module. |
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Keywords: | Hilbert module product system weak dilation white noise von Neumann algebra C*-algebra |
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