Algebraic isomorphisms and Jordan derivations of 𝒥-subspace lattice algebras

• Autorzy: Fangyan Lu , Pengtong Li
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 47B48: Operators on Banach algebras
• 47L10: Algebras of operators on Banach spaces and other topological linear spaces
• 47B47: Commutators, derivations, elementary operators, etc.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2003
• Tom: 158
• Numer: 3
• Strony: 287-301

Daty

wydano

2003

Twórcy

autor

Fangyan Lu

• Department of Mathematics, Suzhou University, Suzhou 215006, P.R. China

autor

Pengtong Li

• Department of Mathematics, Nanjing University, Nanjing 210093, P.R. China

Identyfikatory

DOI

10.4064/sm158-3-7