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
| Title | On a localization of the spectrum of a complex Volterra operator |
| Source | Methods Funct. Anal. Topology, Vol. 25 (2019), no. 1, 12-14 |
| MathSciNet |
MR3935579 |
| Milestones | Received 18/08/2018 |
| Copyright | The 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
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},
MRNUMBER = {MR3935579},
URL = {http://mfat.imath.kiev.ua/article/?id=1140},
}
