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Abstract

We study tensor norms and operator ideals related to the ideal $P_{p,σ}$, 1 < p < ∞, 0 < σ < 1, of (p,σ)-absolutely continuous operators of Matter. If α is the tensor norm associated with $P_{p,σ}$ (in the sense of Defant and Floret), we characterize the $(α')^t$-nuclear and $(α')^t$- integral operators by factorizations by means of the composition of the inclusion map $L^r(μ) → L^1(μ) + L^p(μ)$ with a diagonal operator $B_w:L^{∞}(μ) → L^r(μ)$, where r is the conjugate exponent of p'/(1-σ). As an application we study the reflexivity of the components of the ideal $P_{p,σ}$.