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.

### 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},
}

Coming Soon.