Non-linear mixed Jordan triple $1$-$*$-product on von Neumann algebras

Abdul Khan; Mohd Raza; Husain Alhazmi

Makale detayları

Non-linear mixed Jordan triple $1$-$*$-product on von Neumann algebras

Yazarlar:

Abdul Khan | Mohd Raza | Husain Alhazmi

Yayıncı:

Hacettepe University

Ana Başlıklar:

Algebra and Number Theory

Dergi:

Hacettepe Journal of Mathematics and Statistics Vol.54 Issue 2, pp.378-388

Belge Tipi:

Makale

Yayın Tarihi:

4/2025

Belge Dili:

İngilizce

Document ID (Org No.):

2001346353

pISSN:

2651-477X

Anahtar kelimeler:

Özet:

 It is shown that if M and N are two von Neumann algebras, one of which has no central abelian projection with psi: M rightarrow N satisfying mixed Jordan triple 1--product, i.e., psiA circ B bullet CpsiA circ psiB bullet psiC for all A, B, C in M, then there exists a bijective map Psi: M rightarrow N such that PsiApsiIpsiA with psiI2I, whenever psiI is central, and there exist a central projection mathfrakP in M  such that the restriction of psi to M mathfrakP is a linear -isomorphism, and to MI -mathfrakP is a conjugate linear -isomorphism.

 It is shown that if M and N are two von Neumann algebras, one of which has no central abelian projection with psi: M rightarrow N satisfying mixed Jordan triple 1--product, i.e., psiA circ B bullet CpsiA circ psiB bullet psiC for all A, B, C in M, then there exists a bijective map Psi: M rightarrow N such that PsiApsiIpsiA with psiI2I, whenever psiI is central, and there exist a central projection mathfrakP in M  such that the restriction of psi to M mathfrakP is a linear -isomorphism, and to MI -mathfrakP is a conjugate linear -isomorphism.

 It is shown that if M and N are two von Neumann algebras, one of which has no central abelian projection with psi: M rightarrow N satisfying mixed Jordan triple 1--product, i.e., psiA circ B bullet CpsiA circ psiB bullet psiC for all A, B, C in M, then there exists a bijective map Psi: M rightarrow N such that PsiApsiIpsiA with psiI2I, whenever psiI is central, and there exist a central projection mathfrakP in M  such that the restriction of psi to M mathfrakP is a linear -isomorphism, and to MI -mathfrakP is a conjugate linear -isomorphism.

 It is shown that if M and N are two von Neumann algebras, one of which has no central abelian projection with psi: M rightarrow N satisfying mixed Jordan triple 1--product, i.e., psiA circ B bullet CpsiA circ psiB bullet psiC for all A, B, C in M, then there exists a bijective map Psi: M rightarrow N such that PsiApsiIpsiA with psiI2I, whenever psiI is central, and there exist a central projection mathfrakP in M  such that the restriction of psi to M mathfrakP is a linear -isomorphism, and to MI -mathfrakP is a conjugate linear -isomorphism.

Makale detayları

Non-linear mixed Jordan triple $1$-$*$-product on von Neumann algebras

Yazarlar:

Abdul Khan | Mohd Raza | Husain Alhazmi

Yayıncı:

Hacettepe University

Ana Başlıklar:

Algebra and Number Theory

Dergi:

Hacettepe Journal of Mathematics and Statistics Vol.54 Issue 2, pp.378-388

Belge Tipi:

Makale

Yayın Tarihi:

4/2025

Belge Dili:

İngilizce

Document ID (Org No.):

2001346353

pISSN:

2651-477X

prime ring

semiprime ring

normal ring

involution

left ∗-centralizer

Jordan left ∗-centralizer

generalized derivation

Sayı

Makale detayları

Yazarlar: Abdul Khan | Mohd Raza | Husain Alhazmi

Yayıncı: Hacettepe University

Ana Başlıklar: Algebra and Number Theory

Dergi: Hacettepe Journal of Mathematics and Statistics Vol.54 Issue 2, pp.378-388

Belge Tipi: Makale

Yayın Tarihi: 4/2025

Belge Dili: İngilizce

Document ID (Org No.): 2001346353

pISSN: 2651-477X

Sayı

Yazarlar:

Abdul Khan | Mohd Raza | Husain Alhazmi

Yayıncı:

Hacettepe University

Ana Başlıklar:

Algebra and Number Theory

Dergi:

Hacettepe Journal of Mathematics and Statistics Vol.54 Issue 2, pp.378-388

Belge Tipi:

Makale

Yayın Tarihi:

4/2025

Belge Dili:

İngilizce

Document ID (Org No.):

2001346353

pISSN:

2651-477X