Geodesic
On operator ideals related to (p,σ)-absolutely continuous operators
Studia Mathematica, Tome 138 (2000) no. 1, pp. 25-40

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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 $P_{p,σ}$.
DOI : 10.4064/sm-138-1-25-40
Keywords: tensor norms, operator ideals, (p, σ)-absolutely continuous operators, $g_{p, σ}$-nuclear and $g_{p, σ}$ integral operators

J. A. López Molina 1 ; E. A. Sánchez Pérez 1

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J. A. López Molina; E. A. Sánchez Pérez. On operator ideals related to (p,σ)-absolutely continuous operators. Studia Mathematica, Tome 138 (2000) no. 1, pp. 25-40. doi: 10.4064/sm-138-1-25-40

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