UWSpace is currently experiencing technical difficulties resulting from its recent migration to a new version of its software. These technical issues are not affecting the submission and browse features of the site. UWaterloo community members may continue submitting items to UWSpace. We apologize for the inconvenience, and are actively working to resolve these technical issues.
 

Compressions of Compact Tuples

Thumbnail Image

Files

1-s2.0-S0024379518305573-main.pdf (381.01 KB)

Date

2019-03-01

Authors

Passer, Benjamin
Shalit, Orr

Journal Title

Journal ISSN

Volume Title

Publisher

Elsevier

Abstract

We study the matrix range of a tuple of compact operators on a Hilbert space and examine the notions of minimal, nonsingular, and fully compressed tuples. In this pursuit, we refine previous results by characterizing nonsingular compact tuples in terms of matrix extreme points of the matrix range. Further, we find that a compact tuple A is fully compressed if and only if it is multiplicity-free and the Shilov ideal is trivial, which occurs if and only if A is minimal and nonsingular. Fully compressed compact tuples are therefore uniquely determined up to unitary equivalence by their matrix ranges. We also produce a proof of this fact which does not depend on the concept of nonsingularity.

Description

The final publication is available at Elsevier via https://doi.org/10.1016/j.laa.2018.12.002. © 2018. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/

Keywords

matrix convex set, matrix range, matrix extreme point, operator system, structure of compact tuples

LC Keywords

Citation

URI

https://doi.org/10.1016/j.laa.2018.12.002
 http://hdl.handle.net/10012/14299

Collections

Waterloo Research
Pure Mathematics