Invariant subspaces of $R{L}^1$

Abstract

In this note we extend D. Singh and A. A. W. Mehanna's invariant subspace theorem for $R{H}^1$ (the real Banach space of analytic functions in $H^1$ with real Taylor coefficients) to the simply invariant subspaces of $R{L}^1$ (the real Banach space of functions in $L^1$ with real Fourier coefficients).

4 pages