A density theorem on the operator algebra in Pontrjagin space
type: Item
instance of: scholarly article
title: A density theorem on the operator algebra in Pontrjagin space
zbMATH Open document ID: 1012.46030
author: Tong Yusun
published in: Journal of Mathematical Analysis and Applications
publication date: 2002-07-04T00:00:00Z
review text: The author presents a partial extension of Kaplansky's density theorem to operator algebras on Pontrjagin spaces. For an operator algebra \(M\) on such a space, set \(M_1=\{A\in M\mid \sigma (A^*A)\subset K\}\), where \(K\) is the closed unit disk. Also, for a set of operators \(M\), let \(M^s\) denote its strong closure. The main results says that if \(M\) is a norm closed self-adjoint algebra of operators on a Pontrjagin space, then \((M^s)_1 \subset (M_1)^s\).
Mathematics Subject Classification ID: 46C20
Mathematics Subject Classification ID: 46L05
zbMATH DE Number: 1763449
zbMATH Keywords: Kaplansky's density theorem
zbMATH Keywords: Pontrjagin spaces
reviewed by: Khristo N. Boyadzhiev
MaRDI profile type: Publication
full work available at URL: jmaa.2001.7804
OpenAlex ID: W1998207908
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DOI: 10.1006/JMAA.2001.7804
description: scientific article; zbMATH DE number 1763449