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

doi:10.7153/oam-05-10

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

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

4 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 language	English (US)
Pages (from-to)	139-155
Number of pages	17
Journal	Operators and Matrices
Volume	5
Issue number	1
DOIs	https://doi.org/10.7153/oam-05-10
State	Published - 2011

Keywords

Connected
Diagonal
Idempotent
Normalized tight frame
Paving
Projection

ASJC Scopus subject areas

Analysis
Algebra and Number Theory

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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.",

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AU - Kovalev, Leonid V.

AU - Larson, David

AU - Nguyen, Nga

AU - Tener, James E.

PY - 2011

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N2 - 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.

AB - 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.

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KW - Idempotent

KW - Normalized tight frame

KW - Paving

KW - Projection

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ER -

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

Abstract

Keywords

ASJC Scopus subject areas

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