# On the Range and the Kernel of Derivations

• Volume: 32, Issue: 1, page 31-38
• ISSN: 1310-6600

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## Abstract

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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 same inequality if A is a finite operator and commutes with normal operator T. Some related results are also given.

## How to cite

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Bouali, Said, and Bouhafsi, Youssef. "On the Range and the Kernel of Derivations." Serdica Mathematical Journal 32.1 (2006): 31-38. <http://eudml.org/doc/281478>.

@article{Bouali2006,
abstract = {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 same inequality if A is a finite operator and commutes with normal operator T. Some related results are also given.},
author = {Bouali, Said, Bouhafsi, Youssef},
journal = {Serdica Mathematical Journal},
keywords = {Finite Operator; n-multicyclic hyponormal operator; finite operator; -multicyclic hyponormal operator},
language = {eng},
number = {1},
pages = {31-38},
publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},
title = {On the Range and the Kernel of Derivations},
url = {http://eudml.org/doc/281478},
volume = {32},
year = {2006},
}

TY - JOUR
AU - Bouali, Said
AU - Bouhafsi, Youssef
TI - On the Range and the Kernel of Derivations
JO - Serdica Mathematical Journal
PY - 2006
PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences
VL - 32
IS - 1
SP - 31
EP - 38
AB - 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 same inequality if A is a finite operator and commutes with normal operator T. Some related results are also given.
LA - eng
KW - Finite Operator; n-multicyclic hyponormal operator; finite operator; -multicyclic hyponormal operator
UR - http://eudml.org/doc/281478
ER -

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