A Generalised Commutativity Theorem for Pk - Quasihyponormal Operators
نویسنده
چکیده
For Hilbert space operators A and B, let δAB denote the generalised derivation δAB(X) = AX − XB and let 4AB denote the elementary operator4AB(X) = AXB−X. If A is a pk-quasihyponormal operator, A ∈ pk−QH, and B∗ is an either p-hyponormal or injective dominant or injective pk−QH operator (resp., B∗ is an either p-hyponormal or dominant or pk −QH operator), then δAB(X) = 0 =⇒ δA∗B∗(X) = 0 (resp., 4AB(X) = 0 =⇒4A∗B∗(X) = 0).
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