A Formula for the Numerical Range of Elementary Operators. (20th March 2014)

• Record Type: Journal Article
• Authors: Barraa, M.
• Other Names: Lindstrom M. Academic Editor.; Zhu C. Academic Editor.
• Is Part Of: ISRN mathematical analysis. Volume 2014(2014)
• Publication Date: 2014-03-20
• Subjects: Mathematical analysis -- Periodicals; Mathematical analysis; Periodicals; 515
• DOI: 10.1155/2014/246301
• Languages: English
• ISSNs: 2090-4657

Abstract

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.