Essential numerical range of elementary operators
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- by M. Barraa PDF
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Abstract:
Let $A= (A_{1},...,A_{p})$ and $B=(B_{1},...,B_{p})$ denote two $p$-tuples of operators with $A_{i}\in \mathcal L(H)$ and $B_{i}\in \mathcal L(K).$ Let $R_{2,A,B}$ denote the elementary operators defined on the Hilbert-Schmidt class $\mathcal C^{2}(H,K)$ by $R_{2,A,B}(X)=A_{1}XB_{1}+...+A_{p}XB_{p}.$ We show that \[ co\left [(W_{e}(A)\circ W(B))\cup (W(A)\circ W_{e}(B))\right ]\subseteq V_{e}(R_{2,A,B}).\] Here $V_{e}(.)$ is the essential numerical range, $W(.)$ is the joint numerical range and $W_{e}(.)$ is the joint essential numerical range.References
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Additional Information
- M. Barraa
- Affiliation: Département de Mathématiques, Faculté des Sciences Semlalia, Marrakech, Maroc
- Email: barraa@ucam.ac.ma
- Received by editor(s): November 14, 2003
- Received by editor(s) in revised form: February 13, 2004
- Published electronically: December 20, 2004
- Communicated by: Joseph A. Ball
- © Copyright 2004
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 133 (2005), 1723-1726
- MSC (2000): Primary 47B47; Secondary 47A12
- DOI: https://doi.org/10.1090/S0002-9939-04-07672-5
- MathSciNet review: 2120257