Astashkin, S. V.Sunehag, P.2016-02-172016-02-170039-3223http://hdl.handle.net/1885/733712905We 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 Ni is the normed space N with the norm inherited from Xi (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 Tθ=S−2θI (S denotes the shift operator and I the identity) is closed in any ℓp(μ), where the weight μ=(μn)n∈Z satisfies the inequalities μn≤μn+1≤2μn (n∈Z).18 pages© Instytut Matematyczny PAN, 2008interpolationspaces(N0,N1)θ,q(X0,X1)θ,qNψ∈(X0∩X1)∗NinormIvanov and KaltonTθ=S−2θIℓp(μ)μ=(μn)n∈Zμn≤μn+1≤2μn (n∈Z)200810.4064/sm185-2-42016-02-24