  The main result is that there are infinitely many; in fact, a continuum; of
closed ideals in the Banach algebra $L(L_1)$ of bounded linear operators on
$L_1(0,1)$. This answers a question from A. Pietsch's 1978 book "Operator
Ideals". The proof also shows that $L(C[0,1])$ contains a continuum of closed
ideals. Finally, a duality argument yields that $L(\ell_\infty)$ has a
continuum of closed ideals.
