The abstract concept of an elementary operator was recently introduced and studied by other authors. In this paper, we describe the general form of elementary operators between standard subalgebras of J'-subspace lattice algebras. The result can apply to atomic Boolean subspace lattice algebras and pentagon subspace lattice algebras. Throughout, if X is a Banach space by B(X) we mean the algebra of all bounded linear operators on X. The topological dual of X is denoted by X*. For x € X and / 6

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... ', the operator x / is denned by y i-> f(y)x for y e X, which has rank one if and only if both x and / are nonzero. For any non-empty subset L C X, L 1 stands for its annihilator, that is L L = {f € X* : f(x) = 0 for all x € L}. Let £ be a subspace lattice on a Banach space X, that is, a family of (closed) subspaces of X satisfying (i) (0), X e £ and (ii) n 7 L 7 e £, v 7 L 7 e £, for every family {L 7 }r of elements of £, where Vr£ 7 denotes the closed linear span of Upi 7 -The associated subspace lattice algebra Alg£ is the set of all operators in B(X) which leave every subspace in £ invariant. It is easy to see that Alg£ is a unital weakly closed operator algebra. Put