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Factorization of Montel operators

S. Dierolf, P. Domański (1993)

Studia Mathematica

Consider the following conditions. (a) Every regular LB-space is complete; (b) if an operator T between complete LB-spaces maps bounded sets into relatively compact sets, then T factorizes through a Montel LB-space; (c) for every complete LB-space E the space C (βℕ, E) is bornological. We show that (a) ⇒ (b) ⇒ (c). Moreover, we show that if E is Montel, then (c) holds. An example of an LB-space E with a strictly increasing transfinite sequence of its Mackey derivatives is given.

Factorization of operators on C*-algebras

Narcisse Randrianantoanina (1998)

Studia Mathematica

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...

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