On Perturbations of the Isometric Semigroup of Shifts on the Semiaxis
نویسندگان
چکیده
Perturbations (r τt)t≥0 of the semigroup of shifts (τt)t≥0 on L(R+) are studied under the assumption that r τt−τt belongs to a certain Schatten–von Neumann class Sp with p ≥ 1. It is shown that, for the unitary component in the Wold– Kolmogorov decomposition of the cogenerator of the semigroup (r τt)t≥0, any singular spectral type may be achieved by S1-perturbations. An explicit construction is provided for a perturbation with a given spectral type, based on the theory of model spaces of the Hardy space H2. Also, it is shown that an arbitrary prescribed spectral type may be obtained for the unitary component of the perturbed semigroup by a perturbation of class Sp with p > 1. §
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