A description of the Carleman classes of vectors, in particular the Gevrey classes, of a scalar type spectral operator in a reflexive complex Banach space is shown to remain true without the reflexivity requirement. A similar nature description of the entire vectors of exponential type, known for a normal operator in a complex Hilbert space, is generalized to the case of a scalar type spectral operator in a complex Banach space.
Key words: Scalar type spectral operator, normal operator, Carleman classes of vectors.
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Article Information
Title
On the Carleman ultradifferentiable vectors of a scalar type spectral operator
Marat V. Markin, On the Carleman ultradifferentiable vectors of a scalar type spectral operator, Methods Funct. Anal. Topology 21
(2015), no. 4, 361-369.
BibTex
@article {MFAT838,
AUTHOR = {Markin, Marat V.},
TITLE = {On the Carleman ultradifferentiable vectors of a scalar type spectral operator},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {21},
YEAR = {2015},
NUMBER = {4},
PAGES = {361-369},
ISSN = {1029-3531},
MRNUMBER = {MR3469533},
ZBLNUMBER = {06630279},
URL = {http://mfat.imath.kiev.ua/article/?id=838},
}
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