Two tauberian theorems in Banach spaces
Compositio Mathematica, Tome 18 (1967) no. 1-2, pp. 87-93. 
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     author = {Husain, Taqdir},
     title = {Two tauberian theorems in {Banach} spaces},
     journal = {Compositio Mathematica},
     pages = {87--93},
     publisher = {P. Noordhoff N. V., Groningen},
     volume = {18},
     number = {1-2},
     year = {1967},
     mrnumber = {221156},
     zbl = {0158.13604},
     language = {en},
     url = {http://archive.numdam.org/item/CM_1967__18_1-2_87_0/}
}
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Husain, Taqdir. Two tauberian theorems in Banach spaces. Compositio Mathematica, Tome 18 (1967) no. 1-2, pp. 87-93. http://archive.numdam.org/item/CM_1967__18_1-2_87_0/

G.H. Hardy [1] Divergent Series; Clarendon Press, Oxford, 1946. | MR | Zbl

W.B. Jurkat, [2] Ein funktionentheoretischer Beweis für O-Taubersätz bei Potenzreiben; Arch. Math. VII, 1956, pp. 122-125. | MR | Zbl

W.B. Jurkat, [3] Ein funktionentheoretischer Beweis für O-Taubersätze bei den Verfahren von Borel und Euler-Knopp; Ibid, pp. 278-283. | MR | Zbl