On the connected components of the conjugacy class of projectors on ℓp⊕ℓq

Daniele Garrisi

doi:10.1016/j.indag.2016.11.022

On the connected components of the conjugacy class of projectors on ℓ_p⊕ℓ_q

Research output: Journal Publication › Article › peer-review

Abstract

We characterize the projectors P on a Banach space E having the property of being connected to all the other projectors obtained as a conjugation of P. Using this characterization we show an example of a Banach space where the conjugacy class of a projector splits into several path-connected components, and describe the conjugacy classes of projectors onto subspaces of ℓ_p⊕ℓ_q with p≠q.

Original language	English
Pages (from-to)	446-450
Number of pages	5
Journal	Indagationes Mathematicae
Volume	28
Issue number	2
DOIs	https://doi.org/10.1016/j.indag.2016.11.022
Publication status	Published - 1 Apr 2017
Externally published	Yes

Keywords

Components
Conjugation
Projectors

ASJC Scopus subject areas

General Mathematics

Access to Document

10.1016/j.indag.2016.11.022

Cite this

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abstract = "We characterize the projectors P on a Banach space E having the property of being connected to all the other projectors obtained as a conjugation of P. Using this characterization we show an example of a Banach space where the conjugacy class of a projector splits into several path-connected components, and describe the conjugacy classes of projectors onto subspaces of ℓp⊕ℓq with p≠q.",

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AB - We characterize the projectors P on a Banach space E having the property of being connected to all the other projectors obtained as a conjugation of P. Using this characterization we show an example of a Banach space where the conjugacy class of a projector splits into several path-connected components, and describe the conjugacy classes of projectors onto subspaces of ℓp⊕ℓq with p≠q.

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