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Abstrakty
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.
Słowa kluczowe
Kategorie tematyczne
Czasopismo
Rocznik
Tom
Numer
Strony
239-262
Opis fizyczny
Daty
wydano
2007
Twórcy
autor
- 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.
autor
- 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
Bibliografia
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Bibliografia
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Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_4064-sm179-3-3