Characterizations of Unconditionally Convergent and Weakly Unconditionally Cauchy Series via wRp-Summability, Orlicz-Pettis Type Theorems and Compact Summing Operator
Filomat, cilt.36, sa.18, ss.6347-6358, 2022 (SCI-Expanded)
- 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.