Searcharxiv⌕ Search

arXiv subjects

João Carlos da Motta Ferreira

Publications and source records attributed to João Carlos da Motta Ferreira.

4 recordsLinked to original sources
arXiv2022

Mappings preserving sum of triple products on $\ast $-algebras

Let $\mathcal{A}$ and $\mathcal{B}$ be two unital complex $\ast $-algebras such that $\mathcal{A}$ has a nontrivial projection. In this paper, we study the structure of bijective mappings $Φ:\mathcal{A}\rightarrow \mathcal{B}$ preserving sum of triple products $α_{1} ab^{*}c+α_{2} acb^{*}+α_{3} b^{*}ac +α_{4} cab^{*}+α_{5} b^{*}ca+α_{6} cb^{*}a,$ where the scalars $\{α_{k}\}_{k=1}^{6}$ are complex numbers satisfying some conditions. Applications of obtained results are given.

math.RA↗
arXiv2022

Nonlinear maps preserving sums of triple products on $\ast $-algebras

Let $\mathcal{A}$ and $\mathcal{B}$ be two unital complex $\ast $-algebras such that $\mathcal{A}$ has a nontrivial projection. In this paper, we study the structure of bijective nonlinear maps $Φ:\mathcal{A}\rightarrow \mathcal{B}$ preserving sum of triple products $α_{1} abc+α_{2} a^{*}cb^{*}+α_{3} ba^{*}c +α_{4} cab^{*}+α_{5} bca+α_{6} cb^{*}a^{*},$ where the scalars $\{α_{k}\}_{k=1}^{6}$ are complex numbers satisfying some conditions.

math.RA↗
arXiv2020

Mappings preserving product $ab\pm ba^{*}$ on alternative $W^{*}$-factors

Let $\mathcal{A}$ and $\mathcal{B}$ be two alternative $W^{*}$-factors. In this paper, we proved that a bijective mapping $Φ:\mathcal{A}\rightarrow \mathcal{B}$ satisfies $Φ(ab+ba^{*})=Φ(a)Φ(b)+Φ(b)Φ(a)^{*}$ (resp., $Φ(ab-ba^{*})=Φ(a)Φ(b)-Φ(b)Φ(a)^{*}$), for all elements $a,b\in \mathcal{A}$, if and only if $Φ$ is a $\ast $-ring isomorphism.

math.RA↗