A gentle guide to the basics of two projections theory

A. Böttcher; I. M. Spitkovsky

doi:10.1016/j.laa.2009.11.002

A gentle guide to the basics of two projections theory

A. Böttcher, I. M. Spitkovsky

Mathematics

Research output: Contribution to journal › Article › peer-review

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, and Krupnik's theorem on two idempotents in Banach algebras. These two theorems, which deliver the desired results usually very quickly and comfortably, are missing or wrongly cited in many recent publications on the topic, The paper is intended as a gentle guide to the field. The basic theorems are precisely stated, some of them are accompanied by full proofs, others not, but precise references are given in each case, and many examples illustrate how to work with the theorems.

Original language	English (US)
Pages (from-to)	1412-1459
Number of pages	48
Journal	Linear Algebra and Its Applications
Volume	432
Issue number	6
DOIs	https://doi.org/10.1016/j.laa.2009.11.002
State	Published - Mar 1 2010

Keywords

Angle and gap
Idempotent
Skew and oblique projection
Symbol calculus
Two projections
Two subspaces

ASJC Scopus subject areas

Algebra and Number Theory
Numerical Analysis
Geometry and Topology
Discrete Mathematics and Combinatorics

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10.1016/j.laa.2009.11.002

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AB - 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, and Krupnik's theorem on two idempotents in Banach algebras. These two theorems, which deliver the desired results usually very quickly and comfortably, are missing or wrongly cited in many recent publications on the topic, The paper is intended as a gentle guide to the field. The basic theorems are precisely stated, some of them are accompanied by full proofs, others not, but precise references are given in each case, and many examples illustrate how to work with the theorems.

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A gentle guide to the basics of two projections theory

Abstract

Keywords

ASJC Scopus subject areas

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