February Fourier Talks 2018

Bill Johnson

Title:

Closed Ideals in the Banach Algebra of Bounded Linear Operators on Lp(0,1).

Abstract:

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

1. The only non trivial closed ideal in $L\left(L$p), $1\le p < \infty$, 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\left(L$1) (joint with G. Pisier and G. Schechtman).

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

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