Video library: I. Gogic, Elementary operators on Hilbert $C^*$-modules

VIDEO LIBRARY


International Workshop "Hilbert $C^$-Modules Online Weekend" in memory of William L. Paschke (1946–2019)* December 6, 2020 11:10, Moscow, Lomonosov Moscow State University

Elementary operators on Hilbert $C^$-modules I. Gogić University of Zagreb*
Abstract: We extend the well-known notion of elementary operators on $C^$-algebras to Hilbert $C^$-modules. After providing some basic properties, we generalize Mathieu's theorem for elementary operators on $C^$-algebras by showing that the completely bounded norm of any elementary operator on a non-zero Hilbert $A$-module agrees with the Haagerup norm of its corresponding tensor if and only if $A$ is a prime $C^$-algebra. This is joint work with Ljiljana Arambašić (University of Zagreb). Language: English