A1 Refereed original research article in a scientific journal
Structural rigidity of generalised Volterra operators on Hp
Authors: Miihkinen S, Nieminen PJ, Saksman E, Tylli H-O
Publisher: Elsevier Masson SAS
Publication year: 2018
Journal: Bulletin des Sciences Mathématiques
Volume: 148
First page : 1
Last page: 13
Number of pages: 13
ISSN: 0007-4497
DOI: https://doi.org/10.1016/j.bulsci.2018.06.005
Web address : https://doi.org/10.1016/j.bulsci.2018.06.005
Self-archived copy’s web address: https://arxiv.org/abs/1710.01252
We show that the non-compact generalised analytic Volterra operators $T_g$, where $g in BMOA$, have the following structural rigidity property on the Hardy spaces $H^p$ for $1 le p < infty$ and $p
neq 2$: if $T_g$ is bounded below on an infinite-dimensional subspace $M subset H^p$, then $M$ contains a subspace linearly isomorphic to $ell^p$. This implies in particular that any Volterra operator $T_g: H^p to H^p$ is $ell^2$-singular for $p neq 2$.
