Algebraic isomorphisms and Jordan derivations of 𝒥-subspace lattice algebras

Fangyan Lu, and Pengtong Li. "Algebraic isomorphisms and Jordan derivations of 𝒥-subspace lattice algebras." Studia Mathematica 158.3 (2003): 287-301. <http://eudml.org/doc/284786>.

@article{FangyanLu2003,
abstract = {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.},
author = {Fangyan Lu, Pengtong Li},
journal = {Studia Mathematica},
keywords = {-subspace lattice; algebraic isomorphism; quasi-spatiality; Jordan derivation; additive derivation},
language = {eng},
number = {3},
pages = {287-301},
title = {Algebraic isomorphisms and Jordan derivations of 𝒥-subspace lattice algebras},
url = {http://eudml.org/doc/284786},
volume = {158},
year = {2003},
}

TY - JOUR
AU - Fangyan Lu
AU - Pengtong Li
TI - Algebraic isomorphisms and Jordan derivations of 𝒥-subspace lattice algebras
JO - Studia Mathematica
PY - 2003
VL - 158
IS - 3
SP - 287
EP - 301
AB - 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.
LA - eng
KW - -subspace lattice; algebraic isomorphism; quasi-spatiality; Jordan derivation; additive derivation
UR - http://eudml.org/doc/284786
ER -