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Regular methods of summability in some locally convex spaces

Costas Poulios (2009)

Commentationes Mathematicae Universitatis Carolinae

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 spaces...

RUC systems in rearrangement invariant spaces

P. G. Dodds, E. M. Semenov, F. A. Sukochev (2002)

Studia Mathematica

We present necessary and sufficient conditions for a rearrangement invariant function space to have a complete orthonormal uniformly bounded RUC system.

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