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arXiv · 2003.09576

A Schauder basis for $L_2$ consisting of non-negative functions

Daniel Freeman·Alexander M. Powell·Mitchell A. Taylor
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Abstract

We prove that $L_2(\mathbb{R})$ contains a Schauder basis of non-negative functions. Similarly, $L_p(\mathbb{R})$ contains a Schauder basic sequence of non-negative functions such that $L_p(\mathbb{R})$ embeds into the closed span of the sequence. We prove as well that if $X$ is a separable Banach space with the bounded approximation property, then any set in $X$ with dense span contains a quasi-basis (Schauder frame) for $X$. Furthermore, if $X$ is a separable Banach lattice with a bibasis then any set in $X$ with dense span contains a u-frame.

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Daniel Freeman, Alexander M. Powell, Mitchell A. Taylor. 2020-03-21. A Schauder basis for $L_2$ consisting of non-negative functions. https://arxiv.org/abs/2003.09576

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