Geodesic
On Isomorphisms of Locally Convex Spaces With Similar Biorthogonal Systems
Canadian mathematical bulletin, Tome 16 (1973) no. 2, pp. 179-183

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The relationship between bases and isomorphisms (i.e. linear homeomorphisms) between complete metrizable linear spaces has been studied with great interest by Arsove and Edwards (see [1] and [2]). We prove (Theorem 1) that in the case of B-complete barrelled spaces, similar generalized bases imply existence of an isomorphism. This result was also proved by Dyer and Johnson [4], so we do not give a proof. We show (Theorem 6) that if one assumes that the bases are Schauder and similar, then Theorem 1 holds for countably barrelled spaces. We use Theorem 1 to advantage (Theorems 2-5) to show that one can improve some results due to Davis [3]. 
Bozel, F.; Husain, T. On Isomorphisms of Locally Convex Spaces With Similar Biorthogonal Systems. Canadian mathematical bulletin, Tome 16 (1973) no. 2, pp. 179-183. doi: 10.4153/CMB-1973-032-1
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