Factorization of operators on C*-algebras

Randrianantoanina, Narcisse

Studia Mathematica, Tome 129 (1998), p. 273-285 / Harvested from The Polish Digital Mathematics Library

Résumé

Let A be a C*-algebra. We prove that every absolutely summing operator from A into $ℓ_{2}$ factors through a Hilbert space operator that belongs to the 4-Schatten-von Neumann class. We also provide finite-dimensional examples that show that one cannot replace the 4-Schatten-von Neumann class by the p-Schatten-von Neumann class for any p < 4. As an application, we show that there exists a modulus of capacity ε → N(ε) so that if A is a C*-algebra and $T \in Π_{1} (A, ℓ_{2})$ with $π_{1} (T) \leq 1$ , then for every ε >0, the ε-capacity of the image of the unit ball of A under T does not exceed N(ε). This answers positively a question raised by Pełczyński.

Publié le : 1998-01-01

Zbl 0914.47026

EUDML-ID : urn:eudml:doc:216486

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     author = {Narcisse Randrianantoanina},
     title = {Factorization of operators on C*-algebras},
     journal = {Studia Mathematica},
     volume = {129},
     year = {1998},
     pages = {273-285},
     zbl = {0914.47026},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv128i3p273bwm}
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Randrianantoanina, Narcisse. Factorization of operators on C*-algebras. Studia Mathematica, Tome 129 (1998) pp. 273-285. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv128i3p273bwm/

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