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An Inner-Outer Factorization In ℓp With Applications To Arma Processes, Raymond Cheng, William T. Ross

Department of Math & Statistics Faculty Publications

The following inner-outer type factorization is obtained for the sequence space ℓ^p: if the complex sequence F = (F₀, F₁,F₂,...) decays geometrically, then for an p sufficiently close to 2 there exists J and G in ℓ^p such that F = J * G; J is orthogonal in the Birkhoff-James sense to all of its forward shifts SJ, S²J, S³J, ...; J and F generate the same S-invariant subspace of ℓ^p; and G is a cyclic vector for S on ℓ …