# The norm attainment problem for functions of projections

@article{Bttcher2021TheNA,
title={The norm attainment problem for functions of projections},
author={Albrecht B{\"o}ttcher and Ilya M. Spitkovsky},
journal={Archiv der Mathematik},
year={2021},
pages={1-7}
}
• Published 2021
• Mathematics
• Archiv der Mathematik
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. Every skew projection on that Hilbert space is contained in such an algebra and hence the results of the paper also describe functions of skew projections and their adjoints that attain the norm.

#### References

SHOWING 1-10 OF 15 REFERENCES
Operators That Achieve the Norm
• Mathematics
• 2010
In this paper we study the theory of operators on complex Hilbert spaces, which achieve the norm in the unit sphere. We prove important results concerning the characterization of the {\mathcal{AN}Expand
A SPECTRAL CHARACTERIZATION OF OPERATORS
• Mathematics
• 2017
We establish a spectral characterization theorem for the operators on complex Hilbert spaces of arbitrary dimensions that attain their norm on every closed subspace. The class of these operators isExpand
Once more on algebras generated by two projections
We consider von Neumann algebras generated by two arbitrary orthoprojections on a Hilbert space. A canonical decomposition is obtained for elements A of these algebras in terms of the operator angleExpand
A gentle guide to the basics of two projections theory
• Mathematics
• 2010
Abstract This paper is a survey of the basics of the theory of two projections. It contains in particular the theorem by Halmos on two orthogonal projections and Roch, Silbermann, Gohberg, andExpand
TWO SUBSPACES
and the rest. The parts of M and N in the first four are "thoroughly uninteresting". In "the rest", the orthogonal complement of the span of the first four, M and N are in generic position ("positionExpand
Robert Sheckley’s Answerer for two orthogonal projections
• Mathematics
• 2018
The meta theorem of this paper is that Halmos’ two projections theorem is something like Robert Sheckley’s Answerer: no question about the W*- and C*-algebras generated by two orthogonal projectionsExpand
INVERTING THE DIFFERENCE OF HILBERT SPACE PROJECTIONS
1. P. Erdos, Problem 3740, this Monthly 42 (1935), 396. 2. L. J. Mordell, Egy geometriai problema megoldasa (Solution of a geometrical problem), Kozepiskolai Matematikai es Fizikai Lapok 11 (1935),Expand
Idempotent
• model, and Toeplitz operators attaining their norms. arXiv:2101.03585v1
• 2021
Idempotent, model, and Toeplitz operators attaining their norms
• Mathematics
• 2021
Abstract We study idempotent, model, and Toeplitz operators that attain the norm. Notably, we prove that if Q is a backward shift invariant subspace of the Hardy space H 2 ( D ) , then the modelExpand
• Oper. Theory Adv. Appl.
• 2018