On Isomorphisms of Locally Convex Spaces With Similar Biorthogonal Systems
Keyword(s):
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].
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1967 ◽
Vol 15
(4)
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pp. 295-296
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Keyword(s):
1993 ◽
Vol 48
(2)
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pp. 209-249
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1975 ◽
Vol 20
(4)
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pp. 468-482
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1968 ◽
Vol 9
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pp. 111-118
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1993 ◽
Vol 48
(1)
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pp. 1-6
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1977 ◽
Vol 20
(4)
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pp. 317-327
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1973 ◽
Vol 18
(3)
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pp. 167-172
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1991 ◽
Vol 14
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pp. 17-26
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