Generalized shifts through derivations' concept in $\ell^p(τ)$ spaces

Abstract

In the following text for p ∈ [1, ∞], nonzero cardinal number τ , self-map ϕ : τ → τ if there exists N ∈ N such that ϕ −1 (α) has at most N elements for each α < τ , and operators ψ, λ :• is a (ψ, λ)−derivation if and only if there exists r ∈ C τ with ψ = rσϕ ↾ ℓ p (τ ) and λ = ((1)α<τ − r)σϕ ↾ ℓ p (τ ) ,• is a ψ−derivation if and only if ψ = 1 2 σϕ ↾ ℓ p (τ ) , • is not a (Jordan, Jordan triple) derivation.• is a generalized (Jordan, Jordan triple) derivation if and only if ϕ = idτ .