Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4603672 | Linear Algebra and its Applications | 2007 | 9 Pages |
Abstract
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 AlgD is single in the sense that for any A,B∈AlgD, 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.
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