## Tbilisi Mathematical Journal

### Spectrally compact operators

#### Abstract

We define the concept of a spectrally compact operator, and study the basic properties of these operators. We show that the class of spectrally compact operators is strictly contained in the class of compact operators and in the class of spectrally bounded operators. It is also proved that the set of spectrally compact operators on a spectrally normed space $E$ is a right ideal of $\mathrm{SB}(E)$ and in certain cases it is a two sided ideal. We will also study the spectral adjoint of a spectrally compact operator.

#### Note

The authors would like to express their deepest thanks to the referees for valuable comments and suggesting the shorter proof of Theorem 2.10.

#### Article information

Source
Tbilisi Math. J., Volume 3 (2010), 17-25.

Dates
Revised: 13 October 2010
Accepted: 22 November 2010
First available in Project Euclid: 12 June 2018

https://projecteuclid.org/euclid.tbilisi/1528768855

Digital Object Identifier
doi:10.32513/tbilisi/1528768855

Mathematical Reviews number (MathSciNet)
MR2771663

Zentralblatt MATH identifier
1278.47041

#### Citation

Hejazian, Shirin; Rostamani, Mohadeseh. Spectrally compact operators. Tbilisi Math. J. 3 (2010), 17--25. doi:10.32513/tbilisi/1528768855. https://projecteuclid.org/euclid.tbilisi/1528768855