Abstract
Every product system E is associated with a natural Hilbert space L2(E). There is also a natural way of representing E as a concrete product system ε acting on L2(E), and ε is isomorphic to E. In turn, ε is associated with a semigroup of endomorphisms α= {α t : t≥0} of B(L2(E)) as in Proposition 2.4.9. However, this semigroup is not an E0-semigroup because the projections α t (1) decrease to 0 as t → ∞. This chapter focuses on the problem of constructing an E0-semigroup whose product system is isomorphic to E.
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© 2003 Springer Science+Business Media New York
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Arveson, W. (2003). Spectral C*-Algebras. In: Noncommutative Dynamics and E-Semigroups. Springer Monographs in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-0-387-21524-2_4
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DOI: https://doi.org/10.1007/978-0-387-21524-2_4
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-1803-1
Online ISBN: 978-0-387-21524-2
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