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- W2080398277 abstract "Let p = ( p k ) and q = ( q k ) be any sequences of strictly positive numbers. Denote by c 0 ( p ) the set of all complex sequences x = ( x k ) such that . The Köthe–Toeplitz dual of c 0 ( p ) was determined in Theorem 6(4). In the case in which p ∈ l ∞ (the space of all bounded sequences), c 0 ( p ) becomes a locally convex FK space under the paranorm where M = max (1, sup p k ). It has been recently proved by Lascarides(3) that the following three properties are equivalent: (a) p∈c 0 (i.e.p k → 0), (b) c 0 (p) is perfect (in the sense of Köthe-Toeplitz duality), (c) c 0 (p) has the Schur property (i.e. weak and strong sequential convergence are equivalent)." @default.
- W2080398277 created "2016-06-24" @default.
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- W2080398277 date "1972-05-01" @default.
- W2080398277 modified "2023-09-26" @default.
- W2080398277 title "Operators on the generalized entire sequences" @default.
- W2080398277 cites W2096290936 @default.
- W2080398277 doi "https://doi.org/10.1017/s0305004100050763" @default.
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