Independence, infinite dimension, and operators

Abstract In [Appl. Comput. Harmon. Anal., 46 (2019), 664673] O. Christensen and M. Hasannasab observed that assuming the existence of an operator T sending en to e n +1 for all ∈ ℕ (where ( ) ∈ℕ is a sequence vectors) guarantees linearly independent if only dim {e } = ∞. this article, we recover result as particular case general order-theory-based model-theoretic result. We then return context vector spaces show that, want use condition like i ϕ I where countable replacement previous one, conclusion will stay true : → conjugate successor function succ ↦ + 1 defined on ℕ. finally prove tentative generalization result, replace with more sophisticated which have not managed find new application yet.