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CHARACTERIZATIONS OF HIGHER DERIVATIONS AND JORDAN HIGHER DERIVATIONS ON CSL ALGEBRAS

Part of: Special classes of linear operators

Published online by Cambridge University Press:  15 March 2011

JIANKUI LI  and
JIANBIN GUO
JIANKUI LI*
Affiliation:
Department of Mathematics, East China University of Science and Technology, Shanghai 200237, PR China (email: jiankuili@yahoo.com)
JIANBIN GUO
Affiliation:
Department of Mathematics, East China University of Science and Technology, Shanghai 200237, PR China (email: jianbin-guo@163.com)
*
✉For correspondence; e-mail: jiankuili@yahoo.com
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Abstract

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Let ℒ be a commutative subspace lattice and 𝒜=Alg ℒ. It is shown that every Jordan higher derivation from 𝒜 into itself is a higher derivation. We say that D=(δi)i∈ℕ is a higher derivable linear mapping at G if δn(AB)=∑ i+j=nδi(A)δj(B) for all n∈ℕ and A,B∈𝒜 with AB=G. We also prove that if D=(δi)i∈ℕ is a bounded higher derivable linear mapping at 0 from 𝒜 into itself and δn (I)=0 for all n≥1 , or D=(δi)i∈ℕ is a higher derivable linear mapping at I from 𝒜 into itself, then D=(δi)i∈ℕ is a higher derivation.

Keywords

CSL algebrahigher derivable linear mappinghigher derivationJordan higher derivation

MSC classification

Secondary: 47B47: Commutators, derivations, elementary operators, etc.
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 83 , Issue 3 , June 2011 , pp. 486 - 499
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2011

Footnotes

This work is supported by NSF of China.

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