Characterizations of Unconditionally Convergent and Weakly Unconditionally Cauchy Series via wRp-Summability, Orlicz-Pettis Type Theorems and Compact Summing Operator

Karakuş M., Başar F.

Filomat, cilt.36, sa.18, ss.6347-6358, 2022 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 36 Sayı: 18
  • Basım Tarihi: 2022
  • Doi Numarası: 10.2298/fil2218347k
  • Dergi Adı: Filomat
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, zbMATH
  • Sayfa Sayıları: ss.6347-6358
  • Anahtar Kelimeler: Orlicz-Pettis theorem, Strong p-Cesàro summability, uc series
  • Van Yüzüncü Yıl Üniversitesi Adresli: Evet

Özet

In the present paper, we give a new characterization of unconditional convergent series and give some new versions of the Orlicz-Pettis theorem via FQ σ-family and a natural family F with the separation property S1 through wRp-summability which may be considered as a generalization of the well-known strong p-Cesàro summability. Among other results, we obtain a new (weak) compactness criteria for the summing operator.