A Formula for the Numerical Range of Elementary Operators. (20th March 2014) - Barraa, M.
Abstract : Let B H be the algebra of bounded linear operators on a complex Hilbert space H . For k -tuples of elements of B H,   A = A 1, …, A k and B = B 1, …, B k, let R A, B denote the elementary operator on B H defined by R A, B X = ∑ i = 1 k A i X B i . In this paper, we prove the following formula for the numerical range of R A, B : V R A, B, B B H = [ ∪ U ∈ U H W ( ∑ i = 1 k U A i U * B i ) - ] -, where U H is the set of unitary operators.