Decomposition of linear maps into non-separable \(C^*\)-algebras
type: Item
instance of: scholarly article
title: Decomposition of linear maps into non-separable \(C^*\)-algebras
zbMATH Open document ID: 0593.46047
author: Tadasi Huruya
published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University
publication date: 1985-01-01T00:00:00Z
review text: The main result is that a commutative \(C^*\)-algebra B is injective if every self-adjoint bounded linear map \(\phi\) from a \(C^*\)-algebra into B can be expressed in the form \(\phi =\phi^+-\phi^-\) with \(\phi^+,\phi^-\) positive and \(\| \phi \| =\| \phi^+\| +\| \phi^-\|\). A completely bounded map with no positive decomposition into the Calkin algebra is constructed, assuming the Continuum Hypothesis.
Mathematics Subject Classification ID: 46L05
Mathematics Subject Classification ID: 46M10
Mathematics Subject Classification ID: 03E50
zbMATH DE Number: 3953580
zbMATH Keywords: commutative \(C^*\)-algebra
zbMATH Keywords: injective
zbMATH Keywords: self-adjoint bounded linear map
zbMATH Keywords: Calkin algebra
zbMATH Keywords: Continuum Hypothesis
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2977/prims/1195179059
OpenAlex ID: W1700961025
DOI: 10.2977/PRIMS/1195179059
description: scientific article; zbMATH DE number 3953580