On norm closed ideals in $L(\ell _p,\ell _q)$
Studia Mathematica, Tome 179 (2007) no. 3, pp. 239-262
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
It is well known that the only proper non-trivial norm closed ideal in the algebra $L(X)$ for $X=\ell _p$ $(1\le p \infty )$ or $X=c_0$ is the ideal of compact operators. The next natural question is to describe all closed ideals of $L(\ell _p\oplus \ell _q)$ for $1\le p,q \infty $, $p\not =q$, or equivalently, the closed ideals in $L(\ell _p,\ell _q)$ for $p q$. This paper shows that for $1 p 2 q \infty $ there are at least four distinct proper closed ideals in $L(\ell _p,\ell _q)$, including one that has not been studied before. The proofs use various methods from Banach space theory.
Keywords:
known only proper non trivial norm closed ideal algebra ell infty ideal compact operators natural question describe closed ideals ell oplus ell infty equivalently closed ideals ell ell paper shows infty there least distinct proper closed ideals ell ell including has studied before proofs various methods banach space theory
Affiliations des auteurs :
B. Sari 1 ; Th. Schlumprecht 2 ; N. Tomczak-Jaegermann 3 ; V. G. Troitsky 3
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author = {B. Sari and Th. Schlumprecht and N. Tomczak-Jaegermann and V. G. Troitsky},
title = {On norm closed ideals in $L(\ell _p,\ell _q)$},
journal = {Studia Mathematica},
pages = {239--262},
publisher = {mathdoc},
volume = {179},
number = {3},
year = {2007},
doi = {10.4064/sm179-3-3},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/sm179-3-3/}
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B. Sari; Th. Schlumprecht; N. Tomczak-Jaegermann; V. G. Troitsky. On norm closed ideals in $L(\ell _p,\ell _q)$. Studia Mathematica, Tome 179 (2007) no. 3, pp. 239-262. doi: 10.4064/sm179-3-3
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