Isometric dilations of non-commuting finite rank $n$-tuples
| dc.creator | Davidson, Kenneth R. | |
| dc.creator | Kribs, David W. | |
| dc.creator | Shpigel, Miron E. | |
| dc.date | 2004-11-23 | |
| dc.date.accessioned | 2026-07-07T05:14:37Z | |
| dc.date.available | 2026-07-07T05:14:37Z | |
| dc.description | A contractive $n$-tuple $A=(A_1,...,A_n)$ has a minimal joint isometric dilation $S=(S_1,...,S_n)$ where the $S_i$'s are isometries with pairwise orthogonal ranges. This determines a representation of the Cuntz-Toeplitz algebra. When $A$ acts on a finite dimensional space, the \wot-closed nonself-adjoint algebra $\mathfrak{S}$ generated by $S$ is completely described in terms of the properties of $A$. This provides complete unitary invariants for the corresponding representations. In addition, we show that the algebra $\mathfrak{S}$ is always hyper-reflexive. In the last section, we describe similarity invariants. In particular, an $n$-tuple $B$ of $d\times d$ matrices is similar to an irreducible $n$-tuple $A$ if and only if a certain finite set of polynomials vanish on $B$. | |
| dc.description | 46 pages, preprint version | |
| dc.identifier | https://arxiv.org/abs/math/0411521 | |
| dc.identifier | http://arxiv.org/abs/math/0411521 | |
| dc.identifier | Can. J. Math. 53 (2001), 506-545 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/73345 | |
| dc.subject | Operator Algebras | |
| dc.subject | Functional Analysis | |
| dc.title | Isometric dilations of non-commuting finite rank $n$-tuples | |
| dc.type | text |