It is shown that every algebraic isomorphism between standard subalgebras of 𝒥-subspace lattice algebras is quasi-spatial and every Jordan derivation of standard subalgebras of 𝒥-subspace lattice algebras is an additive derivation. Also, it is proved that every finite rank operator in a 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 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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm158-3-7,
author = {Fangyan Lu and Pengtong Li},
title = {Algebraic isomorphisms and Jordan derivations of J-subspace lattice algebras},
journal = {Studia Mathematica},
volume = {157},
year = {2003},
pages = {287-301},
zbl = {1065.47037},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm158-3-7}
}
Fangyan Lu; Pengtong Li. Algebraic isomorphisms and Jordan derivations of 𝒥-subspace lattice algebras. Studia Mathematica, Tome 157 (2003) pp. 287-301. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm158-3-7/