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ISSN 1088-6826(e) ISSN 0002-9939(p)

Essential numerical range of elementary operators

Author(s): M. Barraa
Journal: Proc. Amer. Math. Soc. 133 (2005), 1723-1726.
MSC (2000): Primary 47B47; Secondary 47A12
Posted: December 20, 2004
MathSciNet review: 2120257
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Abstract | References | Similar articles | Additional information

Abstract: Let $A= (A_{1},...,A_{p})$ and $B=(B_{1},...,B_{p})$ denote two -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

$\begin{displaymath}co\left[(W_{e}(A)\circ W(B))\cup (W(A)\circ W_{e}(B))\right]\subseteq V_{e}(R_{2,A,B}).\end{displaymath}$

Here $V_{e}(.)$ is the essential numerical range,

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

DOI: 10.1090/S0002-9939-04-07672-5
PII: S 0002-9939(04)07672-5
Keywords: Elementary operators, essential numerical range, Hilbert-Schmidt class
Received by editor(s): November 14, 2003
Received by editor(s) in revised form: February 13, 2004
Posted: December 20, 2004
Communicated by: Joseph A. Ball
Copyright of article: Copyright 2004, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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