It is well known that the only proper non-trivial norm closed ideal in the algebra L(X) for (1 ≤ p < ∞) or X = c₀ is the ideal of compact operators. The next natural question is to describe all closed ideals of for 1 ≤ p,q < ∞, p ≠ q, or equivalently, the closed ideals in for p < q. This paper shows that for 1 < p < 2 < q < ∞ there are at least four distinct proper closed ideals in , including one that has not been studied before. The proofs use various methods from Banach space theory.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm179-3-3,
author = {B. Sari and Th. Schlumprecht and N. Tomczak-Jaegermann and V. G. Troitsky},
title = {On norm closed ideals in $L(l\_{p},l\_{q})$
},
journal = {Studia Mathematica},
volume = {178},
year = {2007},
pages = {239-262},
zbl = {1116.47058},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm179-3-3}
}
B. Sari; Th. Schlumprecht; N. Tomczak-Jaegermann; V. G. Troitsky. On norm closed ideals in $L(ℓ_{p},ℓ_{q})$
. Studia Mathematica, Tome 178 (2007) pp. 239-262. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm179-3-3/