Open Access

Berezin number of operators and related questions

Abstract

We prove some estimates for the Berezin number of operators on the reproducing kernel Hilbert spaces. We also give in terms of Berezin number necessary and sufficient conditions providing unitarity of invertible operator on the reproducing kernel Hilbert space. Moreover, we give a lower estimate for any operator on the Hardy space $H^{2}\left( \mathbb{D} \right)$ over the unit disc $\mathbb{D}.$

Key words: Berezin symbol, Berezin number, unitary operator, reproducing kernel Hilbert space, Teoplitz operator.

Article Information

 Title Berezin number of operators and related questions Source Methods Funct. Anal. Topology, Vol. 19 (2013), no. 1, 68-72 MathSciNet MR3088319 zbMATH 1289.47049 Milestones Received 11/06/2012 Copyright The Author(s) 2013 (CC BY-SA)

Authors Information

Mubariz T. Karaev
Institute of Mathematics and Mechanics, National Academy of Sciences of Azerbaijan, Baku, 370141, Azerbaijan

Nizameddin Sh. Iskenderov
Faculty of Mechanics and Mathematics, Baku State University, Baku, 370141, Azerbaijan

Citation Example

Mubariz T. Karaev and Nizameddin Sh. Iskenderov, Berezin number of operators and related questions, Methods Funct. Anal. Topology 19 (2013), no. 1, 68-72.

BibTex

@article {MFAT662,
AUTHOR = {Karaev, Mubariz T. and Iskenderov, Nizameddin Sh.},
TITLE = {Berezin number of operators and related questions},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {19},
YEAR = {2013},
NUMBER = {1},
PAGES = {68-72},
ISSN = {1029-3531},
MRNUMBER = {MR3088319},
ZBLNUMBER = {1289.47049},
URL = {http://mfat.imath.kiev.ua/article/?id=662},
}