Quantitative estimates for interpolated operators by multidimensional methods.

Fernando Cobos; José María Cordeiro; Antón Martínez

Displaying similar documents to “Quantitative estimates for interpolated operators by multidimensional methods.”

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J. López Molina, E. Sánchez Pérez (2000)

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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...

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Interpolation properties of a scale of spaces.

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A scale of function spaces is considered which proved to be of considerable importance in analysis. Interpolation properties of these spaces are studied by means of the real interpolation method. The main result consists in demonstrating that this scale is interpolated in a way different from that for Lp spaces, namely, the interpolation space is not from this scale.