Best approximations, distance formulas and orthogonality in C-algebras

For a unital \(C^*\)-algebra \(\mathcal A\) and a subspace \(\mathcal B\) of \(\mathcal A\), a characterization for a best approximation to an element of \(\mathcal A\) in \(\mathcal B\) is obtained. As an application, a formula for the distance of an element of \(\mathcal A\) from \(\mathcal B\) ha...

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Bibliographic Details
Published in:arXiv.org 2021-01
Main Authors: Grover, Priyanka, Singla, Sushil
Format: Article
Language:English
Subjects:
Approximation
Mathematical analysis
Orthogonality
Online Access:Get full text
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Summary:For a unital \(C^*\)-algebra \(\mathcal A\) and a subspace \(\mathcal B\) of \(\mathcal A\), a characterization for a best approximation to an element of \(\mathcal A\) in \(\mathcal B\) is obtained. As an application, a formula for the distance of an element of \(\mathcal A\) from \(\mathcal B\) has been obtained, when a best approximation of that element to \(\mathcal B\) exists. Further, a characterization for Birkhoff-James orthogonality of an element of a Hilbert \(C^*\)-module to a subspace is obtained.
ISSN:2331-8422