The norm attainment problem for functions of projections
Albrecht B\"ottcher, Ilya M. Spitkovsky
TL;DR
This paper investigates which operators in a von Neumann algebra generated by two orthogonal projections attain their norm, including functions of skew projections, providing insights into the structure of norm-attaining operators.
Contribution
It characterizes norm-attaining operators within the algebra generated by two orthogonal projections, including functions of skew projections and their adjoints.
Findings
Identifies conditions for norm attainment in the algebra
Describes norm-attaining functions of skew projections
Provides a comprehensive characterization of these operators
Abstract
The paper is concerned with the problem of identifying the norm attaining operators in the von Neumann algebra generated by two orthogonal projections on a Hilbert space. This algebra contains every skew projection on that Hilbert space and hence the results of the paper also describe functions of skew projections and their adjoints that attain the norm.
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