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Title: On the Range and the Kernel of Derivations
Authors: Bouali, Said
Bouhafsi, Youssef
Keywords: Finite Operator
n-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.
ISSN: 1310-6600
Appears in Collections:Volume 32, Number 1

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