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

^*Corresponding author for this work

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

4 Citations (Scopus)

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
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
Publication status	Published - 2011
Externally published	Yes

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title = "Projections and idempotents with fixed diagonal and the homotopy problem for unit tight frames",

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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author = "Julien Giol and Kovalev, \{Leonid V.\} and David Larson and Nga Nguyen and Tener, \{James E.\}",

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AU - Giol, Julien

AU - Kovalev, Leonid V.

AU - Larson, David

AU - Nguyen, Nga

AU - Tener, James E.

PY - 2011

Y1 - 2011

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.

KW - Connected

KW - Diagonal

KW - Idempotent

KW - Normalized tight frame

KW - Paving

KW - Projection

UR - https://www.scopus.com/pages/publications/79952414752

U2 - 10.7153/oam-05-10

DO - 10.7153/oam-05-10

M3 - Article

AN - SCOPUS:79952414752

SN - 1846-3886

VL - 5

SP - 139

EP - 155

JO - Operators and Matrices

JF - Operators and Matrices

IS - 1

ER -

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

Abstract

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