arXiv:1811.06571 Abstract | arXiv Analytics

arXiv:1811.06571 [math.FA]Abstract References Reviews Resources

Ideals in $L(L_1)$

William B. Johnson, Gilles Pisier, Gideon Schechtman

Published 2018-11-15, updated 2019-11-13Version 2

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.

Comments: Final version, will appear in Mathematische Annalen

Categories: math.FA

Subjects: 46B03, 46B20, 46B28

Keywords: closed ideals, duality argument yields, banach algebra, bounded linear operators, main result

Related articles: Most relevant | Search more

arXiv:math/0610137 [math.FA] (Published 2006-10-04, updated 2006-10-05)

Derivations into duals of closed ideals of Banach algebras

M. Eshaghi Gordji, B. Hayati, S. A. R. Hosseiniun

arXiv:2003.11414 [math.FA] (Published 2020-03-25)

The number of closed ideals in $L(L_p)$

William B. Johnson, Gideon Schechtman

arXiv:0904.4102 [math.FA] (Published 2009-04-27)