Displaying similar documents to “Banach-Mackey, locally complete spaces, and ℓ p , q -summability.”

Banach-Mackey spaces.

Qiu, Jing Hui, McKennon, Kelly (1991)

International Journal of Mathematics and Mathematical Sciences

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On an inclusion theorem.

Bor, Hüseyin (2000)

International Journal of Mathematics and Mathematical Sciences

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Regular methods of summability in some locally convex spaces

Costas Poulios (2009)

Commentationes Mathematicae Universitatis Carolinae

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Suppose that X is a Fréchet space, 〈 a i j 〉 is a regular method of summability and ( x i ) is a bounded sequence in X . We prove that there exists a subsequence ( y i ) of ( x i ) such that: either (a) all the subsequences of ( y i ) are summable to a common limit with respect to 〈 a i j 〉 ; or (b) no subsequence of ( y i ) is summable with respect to 〈 a i j 〉 . This result generalizes the Erdös-Magidor theorem which refers to summability of bounded sequences in Banach spaces. We also show that two analogous results for some ω 1 -locally convex...