Convexity and weak closedness of the image of operator balls under linear-fractional transformations
type: Item
instance of: scholarly article
title: Convexity and weak closedness of the image of operator balls under linear-fractional transformations
zbMATH Open document ID: 1027.47030
DOI: 10.1007/BF02686253
author: R. Smith
published in: Mathematical Notes
publication date: 2004-01-15T00:00:00Z
review text: The unit ball consists of operators \(S\in L({\mathcal H}^+,{\mathcal H}^-)\), where \({\mathcal H}= {\mathcal H}^+\oplus{\mathcal H}^-\) is a Hilbert (Krein) space. The fractional function \((T_{21}+ T_{22}S)(T_{11}+ T_{12}S)^{-1}\) involves the blocks of \(T:{\mathcal H}\to{\mathcal H}\). Using a decomposition of the bistrict plus operators, the authors prove that the image of the unit ball through a fractional transformation is a convex and closed set in the weak operator topology.
reviewed by: Trandafir Balan
Mathematics Subject Classification ID: 47B50
Mathematics Subject Classification ID: 46C20
zbMATH DE Number: 1517709
zbMATH Keywords: Krein spaces
zbMATH Keywords: fractional functions in Hilbert spaces
zbMATH Keywords: plus operators
MaRDI profile type: Publication
cites work: Operator fractional-linear transformations: convexity and compactness of image; applications
cites work: Q3746364
full work available at URL: https://doi.org/10.1007/bf02686253
OpenAlex ID: W2089112010
description: scientific article; zbMATH DE number 1517709