Please use this identifier to cite or link to this item: http://hdl.handle.net/10525/2501

 Title: On the Range and the Kernel of Derivations Authors: Bouali, SaidBouhafsi, Youssef Keywords: Finite Operatorn-multicyclic hyponormal operator Issue Date: 2006 Publisher: Institute of Mathematics and Informatics Bulgarian Academy of Sciences Citation: Serdica Mathematical Journal, Vol. 32, No 1, (2006), 31p-38p Abstract: 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 same inequality if A is a finite operator and commutes with normal operator T. Some related results are also given. Description: 2000 Mathematics Subject Classification: Primary 47B47, 47B10; Secondary 47A30. URI: http://hdl.handle.net/10525/2501 ISSN: 1310-6600 Appears in Collections: Volume 32, Number 1

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