Algebraic isomorphisms and strongly double triangle subspace lattices

作者：Pang Yongfeng; Ji Guoxing^*

来源：Linear Algebra and Its Applications, 2007, 422(1): 265-273.

DOI：10.1016/j.laa.2006.10.002

• algebraic isomorphism
• rank two operator
• strongly double triangle subspace lattice

Let D = {{0}, K, L, M, X) be a strongly double triangle subspace lattice on a non-zero complex reflexive Banach space X, which means that at least one of three sums K + L, L + M and M + K is closed. It is proved that a non-zero element S of Alg D is single in the sense that for any A, B epsilon Alg D, either AS = O or SB = 0 whenever ASB = 0, if and only if S is of rank two. We also show that every algebraic isomorphism between two strongly double triangle subspace lattice algebras is quasi-spatial.

• 出版日期2007-4-1
• 单位西安建筑科技大学; 陕西师范大学