On cluster systems of tensor product systems of Hilbert spaces
Copyright policy )On cluster systems of tensor product systems of Hilbert spaces
It is known that the spatial product of two product systems is intrinsic. Here we extend this result by analyzing subsystems of the tensor product of product systems. A relation with cluster systems is established. In a special case, we show that the amalgamated product of product systems through strictly contractive units is independent of the choices of the units. The amalgamated product in this case is isomorphic to the tensor product of the spatial product of the two and the type I product system of index one.
9 pages
Mathematics - Functional Analysis, $E_0$-semigroup, 46L55, FOS: Mathematics, 46C05, Primary 46L55, Secondary 46C05, product system, completely positive semigroup, Functional Analysis (math.FA)
Mathematics - Functional Analysis, $E_0$-semigroup, 46L55, FOS: Mathematics, 46C05, Primary 46L55, Secondary 46C05, product system, completely positive semigroup, Functional Analysis (math.FA)
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