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2010 Spectrally compact operators
Shirin Hejazian, Mohadeseh Rostamani
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Tbilisi Math. J. 3: 17-25 (2010). DOI: 10.32513/tbilisi/1528768855


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.


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Shirin Hejazian. Mohadeseh Rostamani. "Spectrally compact operators." Tbilisi Math. J. 3 17 - 25, 2010.


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

zbMATH: 1278.47041
MathSciNet: MR2771663
Digital Object Identifier: 10.32513/tbilisi/1528768855

Primary: 47B48
Secondary: 46B99, 47L10

Rights: Copyright © 2010 Tbilisi Centre for Mathematical Sciences


Vol.3 • 2010
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