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Ideals in $L(L_1)$
- Publication Year :
- 2018
-
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.<br />Comment: Final version, will appear in Mathematische Annalen
- Subjects :
- Mathematics - Functional Analysis
46B03, 46B20, 46B28
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1811.06571
- Document Type :
- Working Paper