A perturbation problem for the shift semigroup

Details A perturbation problem for the shift semigroup A perturbation problem for the shift semigroup

2007-02-15

arxiv.org/abs/math/0702439v1

Mathematics

Operator Algebras

Scientific paper

Motivated by B. Tsirelson's construction of $E_0$-semigroups of type III, we
investigate a $C_0$-semigroup acting on the space of square integrable
functions of the half line whose difference from the shift semigroup is a
Hilbert-Schmidt operator. We give a description of such semigroups in terms of
analytic functions on the right-half plane and construct several examples.

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