Algebraic isomorphisms and Jordan derivations of ${\cal J}$-subspace lattice algebras

Fangyan Lu ¹   ; Pengtong Li ²

¹ Department of Mathematics Suzhou University Suzhou 215006, P.R. China
² Department of Mathematics Nanjing University Nanjing 210093, P.R. China

Studia Mathematica, Tome 158 (2003) no. 3, pp. 287-301

Résumé

It is shown that every algebraic isomorphism between standard subalgebras of ${\mathcal J}$-subspace lattice algebras is quasi-spatial and every Jordan derivation of standard subalgebras of ${\mathcal J}$-subspace lattice algebras is an additive derivation. Also, it is proved that every finite rank operator in a ${\mathcal J}$-subspace lattice algebra can be written as a finite sum of rank one operators each belonging to that algebra. As an additional result, a multiplicative bijection of a ${\mathcal J}$-subspace lattice algebra onto an arbitrary ring is proved to be automatically additive. Those results can be applied to atomic Boolean subspace lattice algebras and pentagon subspace lattice algebras.

Détail

DOI : 10.4064/sm158-3-7

Keywords: shown every algebraic isomorphism between standard subalgebras mathcal subspace lattice algebras quasi spatial every jordan derivation standard subalgebras mathcal subspace lattice algebras additive derivation proved every finite rank operator mathcal subspace lattice algebra written finite sum rank operators each belonging algebra additional result multiplicative bijection mathcal subspace lattice algebra arbitrary ring proved automatically additive those results applied atomic boolean subspace lattice algebras pentagon subspace lattice algebras