# Wydawnictwa / Czasopisma IMPAN / Studia Mathematica / Wszystkie zeszyty

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

### Tom 158 / 2003

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

#### Streszczenie

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.

#### Autorzy

• Fangyan LuDepartment of Mathematics
Suzhou University
Suzhou 215006, P.R. China
e-mail
• Pengtong LiDepartment of Mathematics
Nanjing University
Nanjing 210093, P.R. China
e-mail
e-mail

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