Closed Ideals in the Banach Algebra of Bounded Linear Operators on Lp(0,1).
I'll discuss the Banach algebra structure of the spaces of bounded linear operators on lp and LpLp(0,1). The main new results are
1. The only non trivial closed ideal in , , 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 (joint with G. Pisier and G. Schechtman).
The second result answers a question from the 1978 book of A. Pietsch, "Operator ideals".