The numerical range of elementary operators |
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Authors: | A Seddik |
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Institution: | (1) Department of Mathematics, University of Sana'a Faculty of Science, P.O. Box 14026, Sana'a, Yemen |
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Abstract: | For n-tuplesA=(A
1,...,A
n
) andB=(B
1,...,B
n
) of operators on a Hilbert spaceH, letR
A,B
denote the operator onL(H) defined by
. In this paper we prove that whereW is the joint spatial numerical range andW
0 is the numerical range. We will show also that this inclusion becomes an equality whenR
A,B
is taken to be a generalized derivation, and it is strict whenR
A,B
is taken to be an elementary multiplication operator induced by non scalar self-adjoints operators. |
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Keywords: | AMS classification" target="_blank">AMS classification 47A12 47B47 |
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