Tbilisi Mathematical Journal

Spectrally compact operators

Shirin Hejazian and Mohadeseh Rostamani

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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.


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

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

Received: 27 March 2010
Revised: 13 October 2010
Accepted: 22 November 2010
First available in Project Euclid: 12 June 2018

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 47B48: Operators on Banach algebras
Secondary: 46B99: None of the above, but in this section 47L10: Algebras of operators on Banach spaces and other topological linear spaces

spectrally normed space spectrally bounded operator spectrally compact operator


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

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