Summing multi-norms defined by Orlicz spaces and symmetric sequence space

• Autorzy: Blasco O.

Identyfikatory

DOI

10.14708/cm.v56i1.1105

• Języki publikacji: EN

Abstrakty

EN

We develop the notion of the (X₁,X₂)-summing power-norm based on a~Banach space E, where X₁ and X₂ are symmetric sequence spaces. We study the particular case when X₁ and X₂ are Orlicz spaces ℓ_Φ and ℓ_Ψ respectively and analyze under which conditions the (Φ,Ψ)-summing power-norm becomes a~multinorm. In the case when E is also a~symmetric sequence space L, we compute the precise value of ∥(δ₁,⋯,δ_n)∥n^(X₁,^X₂), where (δ_k) stands for the canonical basis of L, extending known results for the (p,q)-summing power-norm based on the space ℓr which corresponds to X₁=ℓp, X₂=ℓ_q, and E=ℓ_r.

Słowa kluczowe

EN

multinorms; (p,q)-summing norm; Orlicz space; symmetric sequence space

• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Commentationes Mathematicae
• Rocznik: 2016
• Tom: Vol 56, No. 1
• Strony: 145--168
• Opis fizyczny: Bibliogr. 18 poz.

Twórcy

autor

Blasco O.

• Departamento de Analisis Matematico, Universidad de Valencia, 46100 Burjassot, Valencia, Spain

Bibliografia

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Uwagi

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę.