Projections and idempotents with fixed diagonal and the homotopy problem for unit tight frames

Julien Giol, Leonid V. Kovalev, David Larson, Nga Nguyen, James E. Tener

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

We investigate the topological and metric structure of the set of idempotent operators and projections which have prescribed diagonal entries with respect to a fixed orthonormal basis of a Hilbert space. As an application, we settle some cases of conjectures of Larson, Dykema, and Strawn on the connectedness of the set of unit-norm tight frames.

Original languageEnglish (US)
Pages (from-to)139-155
Number of pages17
JournalOperators and Matrices
Volume5
Issue number1
DOIs
StatePublished - 2011

Keywords

  • Connected
  • Diagonal
  • Idempotent
  • Normalized tight frame
  • Paving
  • Projection

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory

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