✦ LIBER ✦
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
No coin nor oath required. For personal study only.
✦ 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.