Compressions of compact tuples

Benjamin Passer, Orr Moshe Shalit

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

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.

Original languageEnglish
Pages (from-to)264-283
Number of pages20
JournalLinear Algebra and Its Applications
Volume564
DOIs
StatePublished - 1 Mar 2019
Externally publishedYes

Keywords

  • Matrix convex set
  • Matrix extreme point
  • Matrix range
  • Operator system
  • Structure of compact tuples

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Numerical Analysis
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics

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