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

López Molina, J.; Sánchez Pérez, E.

Studia Mathematica, Tome 141 (2000), p. 25-40 / Harvested from The Polish Digital Mathematics Library

Résumé

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 of the ideal $P_{p, σ}$ .

Publié le : 2000-01-01

Zbl 0963.46048

EUDML-ID : urn:eudml:doc:216688

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     author = {J. L\'opez Molina and E. S\'anchez P\'erez},
     title = {On operator ideals related to (p,$\sigma$)-absolutely continuous operators},
     journal = {Studia Mathematica},
     volume = {141},
     year = {2000},
     pages = {25-40},
     zbl = {0963.46048},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv138i1p25bwm}
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López Molina, J.; Sánchez Pérez, E. On operator ideals related to (p,σ)-absolutely continuous operators. Studia Mathematica, Tome 141 (2000) pp. 25-40. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv138i1p25bwm/

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