Continuity properties of Hyperlat and reducing subspaces
type: Item
instance of: scholarly article
title: Continuity properties of Hyperlat and reducing subspaces
zbMATH Open document ID: 0709.15001
DOI: 10.1016/0024-3795(90)90322-4
published in: Linear Algebra and its Applications
publication date: 1990-01-01T00:00:00Z
full work available at URL: http://hdl.handle.net/1828/2533
review text: Let V be a finite dimensional complex vector space of dimension \(n\geq 2\), and let A be a linear operator on V. A subspace M is hyperinvariant if it is invariant under every linear operator which commutes with A. Further M is reducing if it is invariant and has an invariant complement. Let RED be the set valued map which associates with each linear transformation A the set of all reducing subspaces. Define HYPERLAT similarly. The author determines the points of continuity, upper semicontinuity, and lower semicontinuity of these two set valued maps.
Mathematics Subject Classification ID: 15A04
zbMATH DE Number: 4165067
zbMATH Keywords: hyperinvariant subspace
zbMATH Keywords: invariant subspace
zbMATH Keywords: linear operator
zbMATH Keywords: reducing subspaces
zbMATH Keywords: continuity
zbMATH Keywords: semicontinuity
zbMATH Keywords: set valued maps
author: Ali-Akbar Jafarian
author: A. R. Sourour
reviewed by: George Phillip Barker
MaRDI profile type: Publication
OpenAlex ID: W2050082979
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description: scientific article; zbMATH DE number 4165067