On the Carleman ultradifferentiable vectors of a scalar type spectral operator (Q2822221)

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 \textit{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.NEWLINENEWLINEIn 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.