Open Access

# On the spectrum of multiplication operators

### Abstract

We study relations between spectra of two operators that are connected to each other through some intertwining conditions. As an application, we obtain new results on the spectra of multiplication operators on $B(\mathcal H)$ relating it to the spectra of the restriction of the operators to the ideal $\mathcal C_2$ of Hilbert-Schmidt operators. We also solve one of the problems, posed in [6], about the positivity of the spectrum of multiplication operators with positive operator coefficients when the coefficients on one side commute. Using the Wiener-Pitt phenomena we show that the spectrum of a multiplication operator with normal coefficients satisfying the Haagerup condition might be strictly larger than the spectrum of its restriction to $\mathcal C_2$.

Key words: Spectrum, multiplication operator, intertwining.

### Article Information

 Title On the spectrum of multiplication operators Source Methods Funct. Anal. Topology, Vol. 24 (2018), no. 3, 265-274 MathSciNet MR3860806 Milestones Received 20/05/2018; Revised 25/05/2018 Copyright The Author(s) 2018 (CC BY-SA)

### Authors Information

V. S. Shulman
Department of Mathematics, Vologda State University, Vologda, Russia

L. Turowska
Department of Mathematical Sciences, Chalmers University of Technology and the University of Gothenburg, Gothenburg SE-412 96, Sweden

### Citation Example

V. S. Shulman and L. Turowska, On the spectrum of multiplication operators, Methods Funct. Anal. Topology 24 (2018), no. 3, 265-274.

### BibTex

@article {MFAT1086,
AUTHOR = {V. S. Shulman and L. Turowska},
TITLE = {On the spectrum of multiplication operators},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {24},
YEAR = {2018},
NUMBER = {3},
PAGES = {265-274},
ISSN = {1029-3531},
MRNUMBER = {MR3860806},
URL = {http://mfat.imath.kiev.ua/article/?id=1086},
}

Coming Soon.