# Factorization of operators on C*-algebras

Studia Mathematica (1998)

• Volume: 128, Issue: 3, page 273-285
• ISSN: 0039-3223

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## Abstract

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Let A be a C*-algebra. We prove that every absolutely summing operator from A into ${\ell }_{2}$ 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 $T\in {\Pi }_{1}\left(A,{\ell }_{2}\right)$ with ${\pi }_{1}\left(T\right)\le 1$, 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.

## How to cite

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Randrianantoanina, Narcisse. "Factorization of operators on C*-algebras." Studia Mathematica 128.3 (1998): 273-285. <http://eudml.org/doc/216486>.

@article{Randrianantoanina1998,
abstract = {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.},
author = {Randrianantoanina, Narcisse},
journal = {Studia Mathematica},
keywords = {C*-algebras; compact operators; Schatten-von Neumann class; -algebra; absolutely summing operator; -capacity},
language = {eng},
number = {3},
pages = {273-285},
title = {Factorization of operators on C*-algebras},
url = {http://eudml.org/doc/216486},
volume = {128},
year = {1998},
}

TY - JOUR
AU - Randrianantoanina, Narcisse
TI - Factorization of operators on C*-algebras
JO - Studia Mathematica
PY - 1998
VL - 128
IS - 3
SP - 273
EP - 285
AB - 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.
LA - eng
KW - C*-algebras; compact operators; Schatten-von Neumann class; -algebra; absolutely summing operator; -capacity
UR - http://eudml.org/doc/216486
ER -

## References

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