Suppose M is a compact Lie Group, is there a Schauder basis for L^1(M)?



About Schauder Basis
Every separable $L\_1$ space is isomorphic to $\ell\_1$ or $L\_1(0,1)$ and thus has a Schauder basis. Look at, for example, Classical Banach spaces by Lindenstrauss and Tzafriri. Other books probably have it, too; see Albiac-Kalton Topics in Banach space theory or Wojtaszczyk's Banach spaces for analysts.


