1. Ideals in $L(L_1)$
- Author
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Johnson, William B., Pisier, Gilles, and Schechtman, Gideon
- Subjects
Mathematics - Functional Analysis ,46B03, 46B20, 46B28 - Abstract
The main result is that there are infinitely many; in fact, a continuum; of closed ideals in the Banach algebra $L(L_1)$ of bounded linear operators on $L_1(0,1)$. This answers a question from A. Pietsch's 1978 book "Operator Ideals". The proof also shows that $L(C[0,1])$ contains a continuum of closed ideals. Finally, a duality argument yields that $L(\ell_\infty)$ has a continuum of closed ideals., Comment: Final version, will appear in Mathematische Annalen
- Published
- 2018