Essential numerical range of elementary operators期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

Essential numerical range of elementary operators

Authors:	M. Barraa

Affiliation:	Département de Mathématiques, Faculté des Sciences Semlalia, Marrakech, Maroc

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 $begin{displaymath}coleft[(W_{e}(A)circ W(B))cup (W(A)circ W_{e}(B))right]subseteq V_{e}(R_{2,A,B}).end{displaymath}$ Here $V_{e}(.)$ is the essential numerical range, is the joint numerical range and $W_{e}(.)$ is the joint essential numerical range.

Keywords:	Elementary operators essential numerical range Hilbert-Schmidt class

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