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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 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 , 2 ) with π 1 ( T ) 1 , then for every ε >0, the ε-capacity of...

Holomorphic automorphism groups in certain compact operator spaces

Carlo Petronio (1990)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

A class of Banach spaces of compact operators in Hilbert spaces is introduced, and the holomorphic automorphism groups of the unit balls of these spaces are investigated.

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