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

Volume 158 / 2003

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


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.


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

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