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Summer 2019 Class of operators with superiorly closed numerical ranges
Mohamed Chraibi Kaadoud
Adv. Oper. Theory 4(3): 673-687 (Summer 2019). DOI: 10.15352/aot.1806-1387

Abstract

‎The aim of this paper is to introduce a class of operators acting on a complex Hilbert space‎. ‎This class contains‎, ‎among others‎, ‎nonzero compact operators‎. ‎We give a characterization of this class in term of generalized numerical ranges and deduce that if $A$ is a compact operator‎, ‎then $ w(A)=\vert \lambda \vert $ with $ \lambda \in\mathit W(A) $‎, ‎where $ \mathit W(A)$ and $ w(A) $ are the numerical range and the numerical radius of $ A $‎, ‎respectively‎. ‎We will give some new necessary conditions for an operator to be compact‎. ‎We also show some light on the generalized numerical ranges of the elementary operators $\delta_{2,A,B}$ and $\mathcal{M}_{2,A,B}$‎.

Citation

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Mohamed Chraibi Kaadoud. "Class of operators with superiorly closed numerical ranges." Adv. Oper. Theory 4 (3) 673 - 687, Summer 2019. https://doi.org/10.15352/aot.1806-1387

Information

Received: 25 June 2018; Accepted: 25 January 2019; Published: Summer 2019
First available in Project Euclid: 2 March 2019

zbMATH: 07056792
MathSciNet: MR3919038
Digital Object Identifier: 10.15352/aot.1806-1387

Subjects:
Primary: 47A12
Secondary: 47B15 , 47B20 , 47B47

Keywords: ‎ ‎numerical radius , ‎ ‎spectral radius , Compact operator , numerical range , spectrum

Rights: Copyright © 2019 Tusi Mathematical Research Group

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Vol.4 • No. 3 • Summer 2019
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