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

• Autorzy: B. Sari , Th. Schlumprecht , N. Tomczak-Jaegermann , V. G. Troitsky
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 47L20: Operator ideals
• 47B37: Operators on special spaces (weighted shifts, operators on sequence spaces, etc.)
• 47B10: Operators belonging to operator ideals (nuclear, p -summing, in the Schatten-von Neumann classes, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2007
• Tom: 179
• Numer: 3
• Strony: 239-262

Daty

wydano

2007

Twórcy

autor

B. Sari

• Department of Mathematics, University of North Texas, Denton, TX 76203-1430, U.S.A.

autor

Th. Schlumprecht

• Department of Mathematics, Texas A&M University, College Station, TX 77843-3368, U.S.A.

autor

N. Tomczak-Jaegermann

• Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB, T6G 2G1, Canada

autor

V. G. Troitsky

• Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB, T6G 2G1, Canada

Identyfikatory

DOI

10.4064/sm179-3-3