McIntosh formula for the gap between regular operators
type: Item
instance of: scholarly article
title: McIntosh formula for the gap between regular operators
zbMATH Open document ID: 1269.46036
published in: Banach Journal of Mathematical Analysis
publication date: 2013-03-20T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.bjma/1358864551
review text: The author gives an alternative definition for the gap between two complemented submodules of a Hilbert \(C^*\)-module using the distance concept as in the case of closed subspaces of a Banach space. He also derives the McIntosh formula for computing the gap of regular operators between Hilbert \(C^*\)-modules. The gap between two closed subspaces of a Hilbert space is defined as the norm of the difference of the orthogonal projections onto these subspaces. The same notion is applied to the graphs of operators to define the gap between two operators. This definition, as it involves projections, is not applicable for closed subspaces of a Banach space. In this case, it is defined in terms of the distance between a point and a subspace.
reviewed by: Mohammad Sal Moslehian
Mathematics Subject Classification ID: 46L08
Mathematics Subject Classification ID: 47A55
Mathematics Subject Classification ID: 47C15
zbMATH DE Number: 6147122
zbMATH Keywords: Hilbert \(C^*\)-module
zbMATH Keywords: gap
zbMATH Keywords: regular operator
zbMATH Keywords: McIntosh formula
author: G. Ramesh
MaRDI profile type: Publication
OpenAlex ID: W2077701856
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DOI: 10.15352/BJMA/1358864551
description: scientific article; zbMATH DE number 6147122