From matrix to operator inequalities (Q2888788)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: From matrix to operator inequalities |
scientific article; zbMATH DE number 6042605
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | From matrix to operator inequalities |
scientific article; zbMATH DE number 6042605 |
Statements
4 June 2012
0 references
\(C^*\)-algebras
0 references
matrices
0 references
bounded operators
0 references
relations
0 references
operator norm
0 references
order
0 references
commutator
0 references
exponential
0 references
residually finite dimensional
0 references
From matrix to operator inequalities (English)
0 references
Defining \(C^*\)-relations and the concepts of being closed and residually finite dimensional, the author presents a meta-theorem: Given a theorem about matrices that states that a residually finite dimensional \(C^*\)-relation implies a closed \(C^*\)-relation, one may conclude that the same implication holds for all bounded operators. Some applications to norms of exponentials and commutators as well as positive noncommutative \(C^*\)-polynomials are given.
0 references
