Continuity of superposition operators on the double sequence spaces Lp

Sağır Duyar B., GÜNGÖR N.

Filomat, cilt.29, sa.9, ss.2107-2118, 2015 (SCI-Expanded, Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 29 Sayı: 9
  • Basım Tarihi: 2015
  • Doi Numarası: 10.2298/fil1509107s
  • Dergi Adı: Filomat
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.2107-2118
  • Anahtar Kelimeler: Continuity, Double sequence spaces, Pringsheim’s convergent, Superposition operators
  • Samsun Üniversitesi Adresli: Hayır

Özet

In this paper, we define the superposition operator Pg where g : N2 * R → R by Pg ((xks)) =g (k; s; xks) for all real double sequence (xks). Chew & Lee [4] and Petranuarat & Kemprasit [7] have characterized Pg : lp → l1 and Pg : lp → lq where 1 ≤ p; q < ∞, respectively. The main goal of this paper is to construct the necessary and sucient conditions for the continuity of Pg : Lp → L1 and Pg : Lp → Lq where 1 _ p; q < ∞.