On norm closed ideals in $L({\ell }_p,{\ell }_q)$

B. Sari, et al. "On norm closed ideals in $L(ℓ_{p},ℓ_{q})$." Studia Mathematica 179.3 (2007): 239-262. <http://eudml.org/doc/285216>.

@article{B2007,
abstract = {It is well known that the only proper non-trivial norm closed ideal in the algebra L(X) for $X = ℓ_\{p\}$ (1 ≤ p < ∞) or X = c₀ is the ideal of compact operators. The next natural question is to describe all closed ideals of $L(ℓ_\{p\}⊕ ℓ_\{q\})$ for 1 ≤ p,q < ∞, p ≠ q, or equivalently, the closed ideals in $L(ℓ_\{p\},ℓ_\{q\})$ for p < q. This paper shows that for 1 < p < 2 < q < ∞ there are at least four distinct proper closed ideals in $L(ℓ_\{p\},ℓ_\{q\})$, including one that has not been studied before. The proofs use various methods from Banach space theory.},
author = {B. Sari, Th. Schlumprecht, N. Tomczak-Jaegermann, V. G. Troitsky},
journal = {Studia Mathematica},
keywords = {operator ideal; sequence spaces},
language = {eng},
number = {3},
pages = {239-262},
title = {On norm closed ideals in $L(ℓ_\{p\},ℓ_\{q\})$},
url = {http://eudml.org/doc/285216},
volume = {179},
year = {2007},
}

TY - JOUR
AU - B. Sari
AU - Th. Schlumprecht
AU - N. Tomczak-Jaegermann
AU - V. G. Troitsky
TI - On norm closed ideals in $L(ℓ_{p},ℓ_{q})$
JO - Studia Mathematica
PY - 2007
VL - 179
IS - 3
SP - 239
EP - 262
AB - It is well known that the only proper non-trivial norm closed ideal in the algebra L(X) for $X = ℓ_{p}$ (1 ≤ p < ∞) or X = c₀ is the ideal of compact operators. The next natural question is to describe all closed ideals of $L(ℓ_{p}⊕ ℓ_{q})$ for 1 ≤ p,q < ∞, p ≠ q, or equivalently, the closed ideals in $L(ℓ_{p},ℓ_{q})$ for p < q. This paper shows that for 1 < p < 2 < q < ∞ there are at least four distinct proper closed ideals in $L(ℓ_{p},ℓ_{q})$, including one that has not been studied before. The proofs use various methods from Banach space theory.
LA - eng
KW - operator ideal; sequence spaces
UR - http://eudml.org/doc/285216
ER -