2-summing multiplication operators

• Autorzy: Dumitru Popa
• Języki publikacji: EN

Abstrakty

EN

Let 1 ≤ p < ∞, $𝒳 = (Xₙ)_{n∈ℕ}$ be a sequence of Banach spaces and $l_{p}(𝒳)$ the coresponding vector valued sequence space. Let $𝒳 = (Xₙ)_{n∈ℕ}$, $𝓨 = (Yₙ)_{n∈ℕ}$ be two sequences of Banach spaces, $𝒱 = (Vₙ)_{n∈ℕ}$, Vₙ: Xₙ → Yₙ, a sequence of bounded linear operators and 1 ≤ p,q < ∞. We define the multiplication operator $M_{𝒱}: l_{p}(𝒳) → l_{q}(𝓨)$ by $M_{𝒱}((xₙ)_{n∈ℕ}) : = (Vₙ(xₙ))_{n∈ℕ}$. We give necessary and sufficient conditions for $M_{𝒱}$ to be 2-summing when (p,q) is one of the couples (1,2), (2,1), (2,2), (1,1), (p,1), (p,2), (2,p), (1,p), (p,q); in the last case 1 < p < 2, 1 < q < ∞.

Kategorie tematyczne

• 47L20: Operator ideals
• 46B45: Banach sequence spaces
• 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: 2013
• Tom: 216
• Numer: 1
• Strony: 77-96

Daty

wydano

2013

Twórcy

autor

Dumitru Popa

• Department of Mathematics, Ovidius University of Constanţa, Bd. Mamaia 124, 900527 Constanţa, Romania

Identyfikatory

DOI

10.4064/sm216-1-6