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Ultraweak Continuity of σ-derivations on von Neumann Algebras
- Source :
- Mathematical Physics, Analysis and Geometry. 12:109-115
- Publication Year :
- 2009
- Publisher :
- Springer Science and Business Media LLC, 2009.
-
Abstract
- Let σ be a surjective ultraweakly continuous ∗-linear mapping and d be a σ-derivation on a von Neumann algebra \(\mathfrak M\). We show that there are a surjective ultraweakly continuous ∗-homomorphism \(\Sigma:\mathfrak M\to\mathfrak M\) and a Σ-derivation \(D:\mathfrak M\to\mathfrak M\) such that D is ultraweakly continuous if and only if so is d. We use this fact to show that the σ-derivation d is automatically ultraweakly continuous. We also prove the converse in the sense that if σ is a linear mapping and d is an ultraweakly continuous ∗-σ-derivation on \(\mathfrak M\), then there is an ultraweakly continuous linear mapping \(\Sigma:\mathfrak M\to\mathfrak M\) such that d is a ∗-Σ-derivation.
- Subjects :
- Discrete mathematics
Pure mathematics
Quantitative Biology::Neurons and Cognition
Mathematics::Operator Algebras
Ultraweak topology
Continuous linear operator
Surjective function
Linear map
symbols.namesake
Von Neumann algebra
Weak operator topology
symbols
Homomorphism
Geometry and Topology
Mathematics::Representation Theory
Mathematical Physics
Mathematics
Von Neumann architecture
Subjects
Details
- ISSN :
- 15729656 and 13850172
- Volume :
- 12
- Database :
- OpenAIRE
- Journal :
- Mathematical Physics, Analysis and Geometry
- Accession number :
- edsair.doi...........8b8ffa79f8aa52a1d8e1a901a7c58e7c