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arXiv · 1811.06571

Ideals in $L(L_1)$

William B. Johnson·Gilles Pisier·Gideon Schechtman
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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.

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William B. Johnson, Gilles Pisier, Gideon Schechtman. 2018-11-15. Ideals in $L(L_1)$. https://arxiv.org/abs/1811.06571

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