Manifolds of frames of projectors

Kovarik, Zdislav V.

doi:10.1016/0024-3795(80)90215-3

Cited by 8 publications

(3 citation statements)

References 4 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…is a collection of self-adjoint projections in H such that p i p j = δ ij p i and i 1 p i = 1. See [2] and [4] for related results on systems of projections. We make the assumption that p i (t) are strongly continuously differentiable, i.e for each fixed ξ ∈ H and i 1, the map I t → p i (t)ξ ∈ H is continuously differentiable.…”

Section: Expectation Onto the Commutant Of A Decompositionmentioning

confidence: 99%

Strongly smooth paths of idempotents

Andruchow

2011

Journal of Mathematical Analysis and Applications

View full text Add to dashboard Cite

It is shown that a curve q(t), t ∈ I (0 ∈ I) of idempotent operators on a Banach space X, which verifies that for each ξ ∈ X, the map t → q(t)ξ ∈ X is continuously differentiable, can be lifted by means of a regular curve Gt, of invertible operators in X: q(t) = Gtq(0)G−1 t , t ∈ I. This is done by using the transport equation of the Grassmannian manifold, introduced by Corach, Porta and Recht. We apply this result to the case when the idempotents are conditional expectations of a C∗ algebra A onto a field of C∗-subalgebras Bt ⊂ A. In this case the invertible operators, restricted to B0, induce C∗-isomorphisms between B0 and Bt. We examine the regularity condition imposed on the curve of expectations, in the case when these expectations are induced by discrete decompositions of a Hilbert space (also called systems of projectors in the literature).Fil: Andruchow, Esteban. Universidad Nacional de General Sarmiento; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderon; Argentin

show abstract

Section: Expectation Onto the Commutant Of A Decompositionmentioning

confidence: 99%

Strongly smooth paths of idempotents

Andruchow

2011

Journal of Mathematical Analysis and Applications

View full text Add to dashboard Cite

show abstract

“…Starting with Halmos and Mc Laughlin [14], who characterized the connected components. Later on, other papers appeared studying geometric or topological aspects of the set of partial isometries, for instance: [16], [18], [19], [1], [2], [4], [8], [9].…”

Section: Introductionmentioning

confidence: 99%

The set of partial isometries as a quotient Finsler space

Andruchow

2022

Indagationes Mathematicae

View full text Add to dashboard Cite

“…Starting with Halmos and Mc Laughlin [12], who characterized the connected components. Later on, other papers appeared studying geometric or topological aspects of the set of partial isometries, for instance: [14], [16], [17], [1], [2], [4].…”

Section: Introductionmentioning

confidence: 99%

The set of partial isometries as a quotient Finsler space

Andruchow¹

2021

Preprint

View full text Add to dashboard Cite

A known general program, designed to endow the quotient space U A /U B of the unitary groups U A , U B of the C * algebras B ⊂ A with an invariant Finsler metric, is applied to obtain a metric for the space I(H) of partial isometries of a Hilbert space H. I(H) is a quotient of the unitary group of B(H) × B(H), where B(H) is the algebra of bounded linear operators in H. Under this program, the solution of a linear best approximation problem leads to the computation of minimal geodesics in the quotient space. We find solutions of this best approximation problem, and study properties of the minimal geodesics obtained.

show abstract

Manifolds of frames of projectors

Cited by 8 publications

References 4 publications

Strongly smooth paths of idempotents

Strongly smooth paths of idempotents

The set of partial isometries as a quotient Finsler space

The set of partial isometries as a quotient Finsler space

Contact Info

Product

Resources

About