Displaying similar documents to “Putnam-Fuglede theorem and the range-kernel orthogonality of derivations.”

On the Range and the Kernel of Derivations

Bouali, Said, Bouhafsi, Youssef (2006)

Serdica Mathematical Journal

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2000 Mathematics Subject Classification: Primary 47B47, 47B10; Secondary 47A30. Let H be a separable infinite dimensional complex Hilbert space and let L(H) denote the algebra of all bounded linear operators on H into itself. Given A ∈ L(H), the derivation δA : L(H)→ L(H) is defined by δA(X) = AX-XA. In this paper we prove that if A is an n-multicyclic hyponormal operator and T is hyponormal such that AT = TA, then || δA(X)+T|| ≥ ||T|| for all X ∈ L(H). We establish the...