Algebraic isomorphisms and strongly double triangle subspace lattices Original Research Article

Let image be a strongly double triangle subspace lattice on a non-zero complex reflexive Banach space image, 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 image is single in the sense that for any image, either AS = 0 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.