|Location:||MSRI: Simons Auditorium|
I'll discuss the Banach algebra structure of the spaces of bounded linear operators on ell_p and L_p:=L_p(0,1).
The main new results are
1. The only non trivial closed ideal in L(L_p), for 1 <= p < infty, 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,