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arXiv · 1612.05049

Complemented basic sequences in Frechet spaces with finite dimensional decomposition

Hasan Gül·Süleyman Onal
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Abstract

Let $E$ be a Frechet-Montel space and $(E_n)_{n \in \mathbb{N}}$ be a finite dimensional unconditional decomposition of $E$ with $\dim(E_n)\leq k$ for some fixed $k \in \mathbb{N}$ and for all $n \in \mathbb{N}$. Consider a sequence $(x_n)_{n \in \mathbb{N}}$ formed by taking an element $x_n$ from each $E_n$ for all $n \in \mathbb{N}$. Then $(x_n)_{n \in \mathbb{N}}$ has a subsequence which is complemented in $E$

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Hasan Gül, Süleyman Onal. 2016-12-15. Complemented basic sequences in Frechet spaces with finite dimensional decomposition. https://arxiv.org/abs/1612.05049

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