Geodesics and near-geodesics in the manifolds of projector frames
type: Item
instance of: scholarly article
title: Geodesics and near-geodesics in the manifolds of projector frames
zbMATH Open document ID: 0642.58008
DOI: 10.1016/0024-3795(88)90136-X
author: Zdislav V. Kovarik
author: Nagwa Sherif
published in: Linear Algebra and its Applications
publication date: 1988-01-01T00:00:00Z
review text: A decomposition of a Banach space into a finite direct sum of subspaces can be represented by its projector frame, which is the ordered set of the corresponding linear projections. The authors consider the space \({\mathcal E}^ n({\mathcal X})\) of all n-frame projectors on a Banach space \({\mathcal X}\). This space can be given the structure of a differentiable manifold with an affine connection. It is proved that interpolation of the classical balanced transformation is close (to cubic order) to a geodesic path in the manifold structure. When a Hilbert space structure is available on the underlying space, the authors obtain a convenient differential equation for the Riemannian geodesics.
Mathematics Subject Classification ID: 58B20
zbMATH DE Number: 4046729
zbMATH Keywords: projector frame
zbMATH Keywords: linear projections
zbMATH Keywords: n-frame projectors
zbMATH Keywords: affine connection
zbMATH Keywords: interpolation
zbMATH Keywords: geodesics
reviewed by: Vagn Lundsgaard Hansen
MaRDI profile type: Publication
cites work: Q5598133
cites work: Q5336643
cites work: Q5332416
cites work: Q5526485
cites work: Manifolds of linear involutions
cites work: Manifolds of frames of projectors
cites work: Characterization of similarities between two n-frames of projectors
cites work: Q5667036
cites work: Q5649693
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description: scientific article; zbMATH DE number 4046729