Banach Journal of Mathematical Analysis

On Jordan centralizers of triangular algebras

Lei Liu

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Abstract

Let A be a unital algebra over a number field F. A linear mapping ϕ from A into itself is called a Jordan-centralized mapping at a given point GA if ϕ(AB+BA)=ϕ(A)B+ϕ(B)A=Aϕ(B)+Bϕ(A) for all A, BA with AB=G. In this paper, it is proved that each Jordan-centralized mapping at a given point of triangular algebras is a centralizer. These results are then applied to some non-self-adjoint operator algebras.

Article information

Source
Banach J. Math. Anal., Volume 10, Number 2 (2016), 223-234.

Dates
Received: 5 April 2015
Accepted: 26 May 2015
First available in Project Euclid: 23 February 2016

Permanent link to this document
https://projecteuclid.org/euclid.bjma/1456246277

Digital Object Identifier
doi:10.1215/17358787-3492545

Mathematical Reviews number (MathSciNet)
MR3465811

Zentralblatt MATH identifier
1338.47039

Subjects
Primary: 47L35: Nest algebras, CSL algebras
Secondary: 47B47: Commutators, derivations, elementary operators, etc. 17B40: Automorphisms, derivations, other operators 17B60: Lie (super)algebras associated with other structures (associative, Jordan, etc.) [See also 16W10, 17C40, 17C50]

Keywords
Jordan centralizer triangular algebra non-self-adjoint operator algebra centralizer

Citation

Liu, Lei. On Jordan centralizers of triangular algebras. Banach J. Math. Anal. 10 (2016), no. 2, 223--234. doi:10.1215/17358787-3492545. https://projecteuclid.org/euclid.bjma/1456246277


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