Geodesic
Characterizations of unconditionally convergent and weakly unconditionally Cauchy series via w r p -summability, Orlicz-Pettis type theorems and compact summing operator
Filomat, Tome 36 (2022) no. 18, p. 6347

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DOI

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 S 1 through w R p-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.
DOI : 10.2298/FIL2218347K
Classification : 46B15, 40A05, 46B45
Keywords: Strong p-Cesàro summability, uc series, Orlicz-Pettis theorem 
Mahmut Karakuş; Feyzi Başar. Characterizations of unconditionally convergent and weakly unconditionally Cauchy series via w r p -summability, Orlicz-Pettis type theorems and compact summing operator. Filomat, Tome 36 (2022) no. 18, p. 6347 . doi: 10.2298/FIL2218347K
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     title = {Characterizations of unconditionally convergent and weakly unconditionally {Cauchy} series via w r p -summability, {Orlicz-Pettis} type theorems and compact summing operator},
     journal = {Filomat},
     pages = {6347 },
     year = {2022},
     volume = {36},
     number = {18},
     doi = {10.2298/FIL2218347K},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2218347K/}
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