Open Access

# On the Carleman ultradifferentiable vectors of a scalar type spectral operator

### Abstract

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.

### Article Information

 Title On the Carleman ultradifferentiable vectors of a scalar type spectral operator Source Methods Funct. Anal. Topology, Vol. 21 (2015), no. 4, 361-369 MathSciNet MR3469533 zbMATH 06630279 Milestones Received 04/06/2015 Copyright The Author(s) 2015 (CC BY-SA)

### Authors Information

Marat V. Markin
Department of Mathematics, California State University, Fresno 5245 N. Backer Avenue, M/S PB 108 Fresno, CA 93740-8001

### Citation Example

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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