Putnam-fuglede Theorem and the Range-kernel Orthogonality of Derivations
نویسنده
چکیده
Let (H) denote the algebra of operators on a Hilbert space H into itself. Let d= δ or , where δAB : (H)→ (H) is the generalized derivation δAB(S)=AS−SB and AB : (H) → (H) is the elementary operator AB(S) = ASB−S. Given A,B,S ∈ (H), we say that the pair (A,B) has the property PF(d(S)) if dAB(S) = 0 implies dA∗B∗(S) = 0. This paper characterizes operators A,B, and S for which the pair (A,B) has property PF(d(S)), and establishes a relationship between the PF(d(S))-property of the pair (A,B) and the range-kernel orthogonality of the operator dAB . 2000 Mathematics Subject Classification. 47A62, 47B47, 47B10.
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