Real method of interpolation on subcouples of codimension one

• Autorzy: S. V. Astashkin , P. Sunehag
• Języki publikacji: EN

Abstrakty

EN

We find necessary and sufficient conditions under which the norms of the interpolation spaces $(N₀,N₁)_{θ,q}$ and $(X₀,X₁)_{θ,q}$ are equivalent on N, where N is the kernel of a nonzero functional ψ ∈ (X₀ ∩ X₁)* and $N_{i}$ is the normed space N with the norm inherited from $X_{i}$ (i = 0,1). Our proof is based on reducing the problem to its partial case studied by Ivanov and Kalton, where ψ is bounded on one of the endpoint spaces. As an application we completely resolve the problem of when the range of the operator $T_{θ} = S - 2^{θ}I$ (S denotes the shift operator and I the identity) is closed in any $ℓ_{p}(μ)$, where the weight $μ = (μₙ)_{n∈ℤ}$ satisfies the inequalities $μₙ ≤ μ_{n+1} ≤ 2μₙ$ (n ∈ ℤ).

Kategorie tematyczne

• 46E30: Spaces of measurable functions ( L p -spaces, Orlicz spaces, K\"othe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
• 46A45: Sequence spaces (including K\"othe sequence spaces)
• 46M35: Abstract interpolation of topological vector spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2008
• Tom: 185
• Numer: 2
• Strony: 151-168

Daty

wydano

2008

Twórcy

autor

S. V. Astashkin

• Department of Mathematics and Mechanics, Samara State University, Acad. Pavlov Street, 443011 Samara, Russia

autor

P. Sunehag

• NICTA, Locked Bag 8001, Canberra, 2601 ACT, Australia

Identyfikatory

DOI

10.4064/sm185-2-4