Factorization of operators on C*-algebras
Studia Mathematica, Tome 128 (1998) no. 3, pp. 273-285
Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences
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 $T ∈ Π_1(A,ℓ_2)$ with $π_1(T) ≤ 1$, 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.
Keywords:
C*-algebras, compact operators
Affiliations des auteurs :
Narcisse Randrianantoanina 1
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author = {Narcisse Randrianantoanina},
title = {Factorization of operators on {C*-algebras}},
journal = {Studia Mathematica},
pages = {273--285},
year = {1998},
volume = {128},
number = {3},
doi = {10.4064/sm-128-3-273-285},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/sm-128-3-273-285/}
}
Narcisse Randrianantoanina. Factorization of operators on C*-algebras. Studia Mathematica, Tome 128 (1998) no. 3, pp. 273-285. doi: 10.4064/sm-128-3-273-285
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