强双三角子空间格代数上Jordan同构的性质

Some properties of Jordan isomorphism on strongly double triangle subspace lattice algebras

目的研究非零复自反的Banach空间上的强双三角子空间格代数的性质。方法利用非零复自反的Banach空间上的强双三角子空间格代数中二秩算子和幂等算子的性质。结果证明了强双三角子空间格代数上的Jordan同构保持二秩算子。结论所给出的关于Jordan同构的性质对于进一步研究强双三角子空间格代数的性质、给出Jordan同构的刻画具有重要作用。

Aim To obtain some properties of Jordan isomorphism on strongly double triangle subspace lattice algebras in a non-zero complex reflexive Banach space.Methods The properties of idempotent operators and rank two operators in strongly double triangle subspace lattice algebras is studied.Results If D is a strongly double triangle subspace lattice in a non-zero complex reflexive Banach space,then every Jordan isomorphism on AlgD preserves rank two operator.Conclusion The results of this study help to study properties of strongly double triangle subspace lattice algebras and disclose characteristic of Jordan isomorphism.