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

### Volume 158 / 2003

Studia Mathematica 158 (2003), 287-301
MSC: 47L10, 47B48, 47B47.
DOI: 10.4064/sm158-3-7

#### Abstract

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.