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The sum of unitary similarity orbits containing only special operators

✍ Scribed by Chi-Kwong Li; Yiu-Tung Poon


Publisher
Elsevier Science
Year
2009
Tongue
English
Weight
172 KB
Volume
431
Category
Article
ISSN
0024-3795

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✦ Synopsis


Let B(H) be the algebra of bounded linear operator acting on a Hilbert space H (over the complex or real field). Characterization is given to A 1 , . . ., A k ∈ B(H) such that for any unitary operators U 1 , . . ., U k , k j=1 U * j A j U j is always in a special class S of operators such as normal operators, self-adjoint operators, unitary operators.

As corollaries, characterizations are given to A ∈ B(H) such that complex, real or nonnegative linear combinations of operators in its unitary orbit U (A) = {U * AU : Uunitary} always lie in S.