# On the Range and the Kernel of Derivations

Bouali, Said; Bouhafsi, Youssef

Serdica Mathematical Journal (2006)

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

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topBouali, 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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