A Formula for the Numerical Range of Elementary Operators
Keyword(s):
Let BH be the algebra of bounded linear operators on a complex Hilbert space H. For k-tuples of elements of BH, A=A1,…,Ak and B=B1,…,Bk, let RA,B denote the elementary operator on BH defined by RA,BX=∑i=1kAiXBi. In this paper, we prove the following formula for the numerical range of RA,B: VRA,B,BBH=[∪U∈UHW(∑i=1kUAiU*Bi)-]-, where UH is the set of unitary operators.
1977 ◽
Vol 29
(5)
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pp. 1010-1030
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1974 ◽
Vol 26
(1)
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pp. 115-120
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2015 ◽
Vol 17
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pp. 1450042
1996 ◽
Vol 53
(3)
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pp. 391-400
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