The number of closed ideals in $L(L_p)$

William B. Johnson, Gideon Schechtman

We show that there are $2^{2^{{\aleph }_0}}$ different closed ideals in the Banach algebra $L(L_p(0,1))$, $1<p\ne 2<\infty$. This solves a problem in A. Pietsch's 1978 book "Operato…