Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
10224097 | Linear Algebra and its Applications | 2019 | 14 Pages |
Abstract
An example due to Pisier shows that two commuting, completely polynomially bounded Hilbert space operators may not be simultaneously similar to contractions. Thus, while each operator is individually similar to a contraction, the pair is not jointly similar to a pair of commuting contractions. We show that this phenomenon does not occur in finite dimensions. More precisely, we show that a finite family of power bounded commuting matrices is always jointly similar to a family of contractions. In fact, the result can be extended to infinite families satisfying certain uniformity conditions. Our approach is based on a joint spectral decomposition of the underlying space.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Raphaël Clouâtre, Diarra Mbacke,