Geodesic
An Abstract Concept of the Sum of a Numerical Series
Canadian journal of mathematics, Tome 22 (1970) no. 4, pp. 863-874

Voir la notice de l'article provenant de la source Cambridge University Press

Our aim in this paper, generally stated, is to formulate an abstract concept of the notion of the sum of a numerical series. More particularly, it is a study of the type of sequence space called “sum space”. The idea of sum space arose in connection with two distinct problems.1.1 The Köthe-Toeplitz dual of a sequence space T consists of all sequences t such that st ∈ l 1 (absolutely summable sequences) for each s∈T. It is known that if cs or bs is used in place of l 1, an analogous theory of duality for sequence spaces can be developed (cf. [2]). What other spaces of sequences can play a rôle analogous to l 1? This problem is treated in [6].1.2. Let {xn , fn } be a complete biorthogonal sequence in (X, X*), where X is a locally convex linear topological space and X* is its topological dual space. 
Ruckle, William H. An Abstract Concept of the Sum of a Numerical Series. Canadian journal of mathematics, Tome 22 (1970) no. 4, pp. 863-874. doi: 10.4153/CJM-1970-098-5
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