Maps preserving zero Jordan products on Hermitian operators

Chebotar, Mikhail A.; Wen, Kuei-Ann; Lee, Pjek Hwee

doi:10.1215/ijm/1258138027

Cited by 12 publications

(2 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In [3], Chebotar et al described maps preserving Jordan zero-products on the Jordan algebra of all Hermitian operators. In [22], Zhao and Hou characterized additive preservers of zeros of Jordan product on certain operator algebras.…”

Section: Introductionmentioning

confidence: 99%

Maps completely preserving commutativity and maps completely preserving Jordan zero-product

Huang

Liu

2014

Linear Algebra and its Applications

View full text Add to dashboard Cite

Let X, Y be real or complex Banach spaces with infinite dimension, and let A, B be standard operator algebras on X and Y , respectively. In this paper, we show that every map completely preserving commutativity from A onto B is a scalar multiple of either an isomorphism or (in the complex case) a conjugate isomorphism. Every map completely preserving Jordan zero-product from A onto B is a scalar multiple of either an isomorphism or (in the complex case) a conjugate isomorphism.

show abstract

Section: Introductionmentioning

confidence: 99%

Maps completely preserving commutativity and maps completely preserving Jordan zero-product

Huang

Liu

2014

Linear Algebra and its Applications

View full text Add to dashboard Cite

show abstract

“…A similar problem, of characterizing Jordan homomorphisms through the action on zero products, has recently also attracted some interest [9,10,14,15]. Our paper is primarily devoted to this topic.…”

Section: Introductionmentioning

confidence: 99%

Characterizing Jordan maps on C*-algebras through zero products

Alaminos¹,

Brešar²,

Extremera³

et al. 2010

Proceedings of the Edinburgh Mathematical Society

View full text Add to dashboard Cite

Let A and B be C * -algebras, let X be an essential Banach A-bimodule and let T : A → B and S : A → X be continuous linear maps with T surjective. Suppose that T (a)T (b) + T (b)T (a) = 0 and S(a)b + bS(a) + aS(b) + S(b)a = 0 whenever a, b ∈ A are such that ab = ba = 0. We prove that then T = wΦ and S = D + Ψ , where w lies in the centre of the multiplier algebra of B, Φ : A → B is a Jordan epimorphism, D : A → X is a derivation and Ψ : A → X is a bimodule homomorphism.

show abstract

Homomorphisms and Related Maps

Brešar

2021

Zero Product Determined Algebras

View full text Add to dashboard Cite

Maps preserving zero Jordan products on Hermitian operators

Cited by 12 publications

References 18 publications

Maps completely preserving commutativity and maps completely preserving Jordan zero-product

Maps completely preserving commutativity and maps completely preserving Jordan zero-product

Characterizing Jordan maps on C*-algebras through zero products

Homomorphisms and Related Maps

Contact Info

Product

Resources

About