Journal article
On closures of joint similarity orbits
Integral equations and operator theory, Vol.8(4), pp.489-556
07/1985
DOI: 10.1007/BF01204700
Abstract
For an n-tuple T=(T1,..., Tn) of operators on a Hilbert spacexxHx, the joint similarity orbit of T isxxSx(T)={VTV−1 =(VT1V−1,...,VTnV−1): V is invertible onxxHx}. We study the structure of the norm closure ofxxSx, both in the case when T is commutative and when it is not. We first develop a Rota-model for the Taylor spectrum and use it to study n-tuples with totally disconnected Taylor spectrum, in particular quasinilpotent ones. We then consider limits of nilpotent n-tuples, and of normal n-tuples. For noncommuting n-tuples, we present a number of surprising facts relating the closure ofxxSx(T) to the Harte spectrum of T and the lack of commutativity of T. We show that a continuous function which is constant onxxSx(T) for all T must be constant. We conclude the paper with a detailed study of closed similarity orbits.
Details
- Title: Subtitle
- On closures of joint similarity orbits
- Creators
- Raúl E Curto - University of Iowa, MathematicsDomingo A Herrero
- Resource Type
- Journal article
- Publication Details
- Integral equations and operator theory, Vol.8(4), pp.489-556
- DOI
- 10.1007/BF01204700
- ISSN
- 0378-620X
- eISSN
- 1420-8989
- Language
- English
- Date published
- 07/1985
- Academic Unit
- Mathematics
- Record Identifier
- 9983986092702771
Metrics
15 Record Views