February Fourier Talks 2018

I'll discuss the Banach algebra structure of the spaces of bounded linear operators on l_p and L_p$\equiv$L_p(0,1). The main new results are

1. The only non trivial closed ideal in $L(L$_p), , that has a left approximate identity is the ideal of compact operators (joint with N. C. Phillips and G. Schechtman).

2. There are infinitely many; in fact, a continuum; of closed ideals in $L(L$₁) (joint with G. Pisier and G. Schechtman).

The second result answers a question from the 1978 book of A. Pietsch, "Operator ideals".