Why the $L^1(R)$ space does not have a unconditional basis. It is a known fact that $L^p(R)$ ($1<p<+\infty$) has unconditional basis. A simple example is the dyadic wavelet or Haar system. I would greatly appreciate it if you can give me some hints of the proof or some related references.
2026-03-25 03:00:40.1774407640
Why the $L^1(R)$ space does not have a unconditional basis
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