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## Studia Mathematica

2007 | 179 | 3 | 239-262
Tytuł artykułu

### On norm closed ideals in $L(ℓ_{p},ℓ_{q})$

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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.
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Tom
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239-262
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wydano
2007
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• Department of Mathematics, University of North Texas, Denton, TX 76203-1430, U.S.A.
autor
• Department of Mathematics, Texas A&M University, College Station, TX 77843-3368, U.S.A.
• Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB, T6G 2G1, Canada
autor
• Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB, T6G 2G1, Canada
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