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Factorization of operators on C*-algebras

100%

Randrianantoanina N.

Studia Mathematica

1998

tom 128

nr 3

273-285

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.

Interpolation by elementary operators

80%

Magajna B.

Studia Mathematica

1993

tom 105

nr 1

77-92

Given two n-tuples $a = (a_1,...,a_n)$ and $b = (b_1,...,b_n)$ of bounded linear operators on a Hilbert space the question of when there exists an elementary operator E such that $Ea_j = b_j$ for all j =1,...,n, is studied. The analogous question for left multiplications (instead of elementary operators) is answered in any C*-algebra A, as a consequence of the characterization of closed left A-submodules in $A^n$.

K-theory from the point of view of C*-algebras and Fredholm representations

51%

Mishchenko A.

Open Mathematics

2005

tom 3

nr 4

766-793

These notes represent the subject of five lectures which were delivered as a minicourse during the VI conference in Krynica, Poland, “Geometry and Topology of Manifolds”, May, 2–8, 2004.

Ograniczanie wyników

2 Studia Mathematica

1 Open Mathematics

1 Magajna B.

1 Mishchenko A.

1 Randrianantoanina N.

1 2005

1 1998

1 1993

Wyniki wyszukiwania

Factorization of operators on C*-algebras

Interpolation by elementary operators

K-theory from the point of view of C*-algebras and Fredholm representations