This is an announcement for the paper “Ideals in $L(L_1)$” by William B.Johnsonhttps://arxiv.org/search/math?searchtype=author&query=Johnson%2C+W+B, Gilles Pisierhttps://arxiv.org/search/math?searchtype=author&query=Pisier%2C+G, Gideon Schechtmanhttps://arxiv.org/search/math?searchtype=author&query=Schechtman%2C+G.
Abstract: 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.
The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1811.06571