Banach ideals on Hilbert spaces

Y. Gordon; D. Lewis

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On operator ideals related to (p,σ)-absolutely continuous operators

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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 $L^{r} (μ) \to L^{1} (μ) + L^{p} (μ)$ with a diagonal operator $B_{w} : L^{\infty} (μ) \to L^{r} (μ)$ , where r is the conjugate exponent of p’/(1-σ). As an application we study the reflexivity of the components...