On the connected components of the conjugacy class of projectors on $ \ell_p\oplus\ell_q $

Daniele Garrisi

doi:10.1016/j.indag.2016.11.022

paper

On the connected components of the conjugacy class of projectors on $ℓ_{p} \oplus ℓ_{q}$

arXiv:0809.1176 · doi:10.1016/j.indag.2016.11.022

Abstract

We characterize the projectors $P$ on a Banach space $E$ having the property of being connected to all the others projectors obtained as a conjugation of $P$ . Using this characterization we show an example of 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 $ℓ_{p} \oplus ℓ_{q}$ with $p \neq = q$ .

arXiv comment5 pages

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

Abstract

On the connected components of the conjugacy class of projectors on $ℓ_{p} \oplus ℓ_{q}$