Article
Ufa Mathematical Journal
Volume 4, Number 1, pp. 16-26
On applications of the model spaces to the construction of cocyclic perturbations of the semigroup of shifts on the semiaxis
Amosov G.G., Baranov A.D., Kapustin V.V.
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We describe a construction of perturbations of the semigroup of shifts on the half-line by means of the theory of model spaces. It is shown that it is possible to choose an inner function generating the model space so that the perturbed semigroup differ from the initial semigroup by an operator from the Schatten--von Neumann class $\mathfrak{S}_p$, $p>1$. A special consideration is given to the case of the trace class operators \medskip $\mathfrak{S}_1$.