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arXiv · 1604.03547

The S-basis and M-basis Problems for Separable Banach Spaces

Tepper L Gill
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Abstract

This note has two objectives. The first objective is show that, even if a separable Banach space does not have a Schauder basis (S-basis), there always exists Hilbert spaces $\mcH_1$ and $\mcH_2$, such that $\mcH_1$ is a continuous dense embedding in $\mcB$ and $\mcB$ is a continuous dense embedding in $\mcH_2$. This is the best possible improvement of a theorem due to Mazur (see \cite{BA} and also \cite{PE1}). The second objective is show how $\mcH_2$ allows us to provide a positive answer to the Marcinkiewicz-basis (M-basis) problem.

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Tepper L Gill. 2016-04-12. The S-basis and M-basis Problems for Separable Banach Spaces. https://arxiv.org/abs/1604.03547

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