Linear maps preserving idempotency of certain operator products on JJ-subspace lattice algebras

Abstract Let L 1 L₁ and L 2 L₂ be J J -subspace lattices on complex Banach spaces X 1 and X 2, respectively, and let Alg L 1 AlgL₁ and Alg L 2 AlgL₂ be the associated J J -subspace lattice algebras. For an integer k ≥ 2, let (i 1, i 2, …, i m) be a finite sequence such that i 1, i 2, …, i m = 1, 2, …, k and at least one of the terms in (i 1, i 2, …, i m) appears exactly once. The generalized product of k operators A 1, A 2, …, A k is defined by A 1 ∗ A 2 ∗ … ∗ A k = A i 1 A i 2