Range kernel orthogonality of derivations

✍ Scribed by B.P. Duggal

• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 66 KB
• Volume: 304
• Category: Article
• ISSN: 0024-3795
• DOI: 10.1016/s0024-3795(99)00193-7

✦ Synopsis

Let H be a separable infinite dimensional complex Hilbert space, and let B(H ) denote the algebra of operators on H into itself. The generalised derivation δ A,B :

and let d A,B denote δ A,B or A,B . Let S ∈ C p (the Schatten p-class, 1 < p < ∞). Given that the pair (A, B) of operators satisfies the property ker d A,B |C p ⊆ ker d A * ,B * | C p , we prove a necessary and sufficient condition for d A * ,B * (X) + S p S p to hold for all X ∈ C p .