The number of closed ideals in the algebra of bounded operators on Lebesgue spaces (Q6119194)

Summary: We survey some of the recent progress in determining the number of two-sided closed ideals in the Banach algebras of bounded linear operators on Lebesgue spaces, \(L_p[0,1]\). In particular, we discuss two recent results: the first of Johnson, Pisier, and the author, showing that there are a continuum of such ideal in the case of \(p=1\); the second a result of Johnson and the author, showing that in the case \(1<p<\infty\), \(p \neq 2\), there are exactly 2 to the continuum such ideals. For the entire collection see [Zbl 07816358].