The Sum of Unitary Similarity Orbits Containing Only Special Operators
نویسندگان
چکیده
Dedicated to Professor Shmuel Friedland. Abstract 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 A1, . . . , Ak ∈ B(H) such that for any unitary operators U1, . . . , Uk, ∑k j=1 U ∗ j AjUj 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 : U unitary} always lie in S.
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