Solvability of new (SSIE) involving the continuous and residual spectra of the generalized difference operator B (r, s) on c₀

• Autorzy: Malafosse Bruno de

Identyfikatory

DOI

10.21008/j.0044-4413.2023.0005

• Języki publikacji: EN

Abstrakty

EN

Let U⁺ be the set of all positive sequences. Then, given any sequence z = (z_n)_n≥1 ∈ U⁺ and any set E of complex sequences, we write E_z for the set of all sequences y = (y_n)_n≥1 such that y/z = (y_n/z_n)_n≥1 ∈ E. We use the notation s_z = (ℓ_∞)_z. In this paper, for given r, s≠ 0 and for every λ ∈ ℂ, we determine the set of all positive sequences x = (x_n)_n≥1 that satisfy the (SSIE) with an operator (c₀)_B(r,s)−λI ⊂ Ɛ + s_x, where Ɛ ⊂ s_θ for some θ ∈ U⁺ is a linear space of sequences, in each of the cases, (1) |λ - r| > |s|, or λ = r, (2) |λ - r| = |s| and (3) |λ - r| < |s| and λ ≠ r. These cases are associated with the continuous and residual spectra σ_c (B (r, s), c₀) and σ_r (B (r, s), c₀), of B (r, s) on c₀, determined by Altay and Başar in [2]. We apply these results to the solvability of the (SSIE) (c₀)_B(r,s)−λI ⊂ s^(c)_R +s_x for all λ ∈ ℂ and R > 0. Then we deal with the (SSIE) (c₀)_Δ−λI ⊂ bv_p + s_x and (c₀)_B(r,s)−λI ⊂ E_Rɑ + s_x, for E = c₀, c, or ℓ_∞, where R_ɑ, ɑ ∈ U⁺, is the Rhaly matrix. These results extend those stated in [21].

Słowa kluczowe

EN

sequence space; BK space; SSIE; Banach algebra; bounded linear operator

• Wydawca: Wydawnictwo Politechniki Poznańskiej
• Czasopismo: Fasciculi Mathematici
• Rocznik: 2023
• Tom: nr 66
• Strony: 61--75
• Opis fizyczny: Bibliogr. 28 poz.

Twórcy

autor

Malafosse Bruno de

• Université du Havre 76600

Bibliografia

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Uwagi

Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023).