Complemented basic sequences in Frechet spaces with finite dimensional decomposition

Hasan Gül; Süleyman Onal

Complemented basic sequences in Frechet spaces with finite dimensional decomposition

Functional Analysis 2016-12-16 v1

Authors: Hasan Gül , Süleyman Onal

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 $E$

Keywords

set theory and dimension theory integer sequences and recurrences

Cite

@article{arxiv.1612.05049,
  title  = {Complemented basic sequences in Frechet spaces with finite dimensional decomposition},
  author = {Hasan Gül and Süleyman Onal},
  journal= {arXiv preprint arXiv:1612.05049},
  year   = {2016}
}

Comments

12 pages

Complemented basic sequences in Frechet spaces with finite dimensional decomposition

Abstract

Keywords

Cite

Comments

Related papers