Solvability of sequence spaces equations of the from (E_a)_Δ + F_x = F_b

• Autorzy: Malafosse B. de

Identyfikatory

DOI

0.1515/fascmath-2015-0018

• Języki publikacji: EN

Abstrakty

EN

Given any sequence a = (a_n)_n≥1 of positive real numbers and any set E of complex sequences, we write E_a for the set of all sequences y = (y_n)_n≥1 such that y/a = (y_n/a_n)>)_n≥1 Є E; in particular, s_a^(c) denotes the set of all sequences y such that y/a converges. For any linear space F of sequences, we have F_x = F_b if and only if x/b and b/x Є M (F, F). The question is: what happens when we consider the perturbed equation Ɛ + F_x = F_b where Ɛ is a special linear space of sequences? In this paper we deal with the perturbed sequence spaces equations (SSE), defined by (E_a)_Δ + s_x^(c) = s_b^(c) where E = c₀, or l_p, (p > 1) and Δ is the operator of the first difference defined by Δ_ny = y_n - y_n-1 for all n ≥ 1 with the convention y>sub>0 = 0. For E = c₀ the previous perturbed equation consists in determining the set of all positive sequences x = (x_n)_n that satisfy the next statement. The condition y_n/b_n → L₁ holds if and only if there are two sequences u, v with y = u + v such that Δ_nu/a_n → 0 and v_n/x_n → L₂ (n → ∞) for all y and for some scalars L₁ and L₂. Then we deal with the resolution of the equation (E_a)_{Δ + sx}⁰ = s_b>⁰ for E = c, or s₁, and give applications to particular classes of (SSE).

Słowa kluczowe

EN

BK space; spaces of strongly bounded sequences; sequence spaces equations; sequence spaces equations with operator

• Wydawca: Wydawnictwo Politechniki Poznańskiej
• Czasopismo: Fasciculi Mathematici
• Rocznik: 2015
• Tom: Nr 55
• Strony: 109--131
• Opis fizyczny: Bibliogr. 17 poz.

Twórcy

autor

Malafosse B. de

• IUT du Havre 76610 Le Havre, France

Bibliografia

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