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On the Carleman ultradifferentiable vectors of a scalar type spectral operator. (English) Zbl 1363.47069

A description of the Carleman classes of ultradifferentiable vectors, in particular the Gevrey classes, of a normal operator on a Hilbert space was given by V. I. Gorbachuk [Ukr. Math. J. 35, 531–543 (1983; Zbl 0541.47021)]. It was extended by the author in [Int. J. Math. Math. Sci. 2004, No. 57-60, 3219–3235 (2004; Zbl 1085.47042)] to the case of a scalar type spectral operator on a reflexive Banach space.
In the paper under review, the author shows that the result remains true without the reflexivity assumption. A similar description is obtained for entire vectors of exponential type.

MSC:

47B40 Spectral operators, decomposable operators, well-bounded operators, etc.
47B15 Hermitian and normal operators (spectral measures, functional calculus, etc.)
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