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.

Full Text

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},
}