# Factorization of operators on C*-algebras

Studia Mathematica (1998)

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

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topRandrianantoanina, 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 -

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