A Schauder basis for $L_1(0,\infty)$ consisting of non-negative functions

TL;DR

This paper constructs a non-negative Schauder basis for the space L_1(0,∞) and explores properties of non-negative sequences in L_p spaces, advancing understanding of basis structures in functional analysis.

Contribution

It introduces a Schauder basis of non-negative functions for L_1(0,∞) and analyzes their unconditional and quasibasic properties in L_p spaces.

Findings

Established a non-negative Schauder basis for L_1(0,∞)

Analyzed unconditional basic sequences of non-negative functions in L_p

Investigated quasibasic sequences of non-negative functions

Abstract

We construct a Schauder basis for $L_1$ consisting of non-negative functions and investigate unconditionally basic and quasibasic sequences of non-negative functions in $L_p$, $1\le p < \infty$.