© Hindawi Publishing Corp. ON THE CARLEMAN CLASSES OF VECTORS OF A SCALAR TYPE SPECTRAL OPERATOR

The Carleman classes of a scalar type spectral operator in a reflexive Banach space are characterized in terms of the operator’s resolution of the identity. A theorem of the Paley-Wiener type is considered as an application. 2000 Mathematics Subject Classification: 47B40, 47B15, 47B25, 30D60. 1. Introduction. As was shown in [8] (see also [9, 10]), under certain conditions, the Carleman classes of vectors of a normal operator in a complex Hilbert space can be characterized in terms of the operator’s spectral measure (the resolution of the identity). The purpose of the present paper is to generalize this characterization to the cas