Open Access

On a localization of the spectrum of a complex Volterra operator


Abstract

A complex Volterra operator with the symbol $g=\log{(1+u(z))}$, where $u$ is an analytic self map of the unit disk $\mathbb D$ into itself is considered. We show that the spectrum of this operator on $H^p(\mathbb D)$, $1\le p<\infty$, is located in the disk $\{\lambda:|\lambda+p/2|\leq p/2\}$.

Key words: Complex Volterra operator, symbol, BMOA, spectrum.


Full Text





Article Information

TitleOn a localization of the spectrum of a complex Volterra operator
SourceMethods Funct. Anal. Topology, Vol. 25 (2019), no. 1, 12-14
MilestonesReceived 18/08/2018
CopyrightThe Author(s) 2019 (CC BY-SA)

Authors Information

Miron B. Bekker
University of Pittsburgh at Johnstown, Johnstown, PA, USA

Joseph A. Cima
Department of Mathematics, The University of North Carolina at Chapell Hill, CB 3250, 329 Phillips Hall, Chapel Hill, NC 27599, USA


Google Scholar Metrics

Citing articles in Google Scholar
Similar articles in Google Scholar

Export article

Save to Mendeley



Citation Example

Miron B. Bekker and Joseph A. Cima, On a localization of the spectrum of a complex Volterra operator, Methods Funct. Anal. Topology 25 (2019), no. 1, 12-14.


BibTex

@article {MFAT1140,
    AUTHOR = {Miron B. Bekker and Joseph A. Cima},
     TITLE = {On a localization of the spectrum of a complex Volterra operator},
   JOURNAL = {Methods Funct. Anal. Topology},
  FJOURNAL = {Methods of Functional Analysis and Topology},
    VOLUME = {25},
      YEAR = {2019},
    NUMBER = {1},
     PAGES = {12-14},
      ISSN = {1029-3531},
       URL = {http://mfat.imath.kiev.ua/article/?id=1140},
}


References

Coming Soon.

All Issues