On contractive projections in Hardy spaces

Beata Randrianantoanina (Miami University; Besan\c{c}on; Eric Ricard (Universit\'e de Franche-Comt\'e; Florence Lancien (Universit\'e de Franche-Comt\'e; France); Ohio; Oxford; USA)

arxiv: math/0504294 · v1 · pith:L2BZGNSFnew · submitted 2005-04-14 · 🧮 math.FA · math.CV

On contractive projections in Hardy spaces

Florence Lancien (Universit\'e de Franche-Comt\'e , Besan\c{c}on , France) , Beata Randrianantoanina (Miami University , Oxford , Ohio , USA) , Eric Ricard (Universit\'e de Franche-Comt\'e This is my paper

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keywords admitinftyprojectionsbasisbiggerconjectureconstantcontractive

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We prove a conjecture of Wojtaszczyk that for $1\leq p<\infty$, $p\neq 2$, $H_p(\mathbbT)$ does not admit any norm one projections with dimension of the range finite and bigger than 1. This implies in particular that for $1\leq p<\infty$, $p\ne 2$, $H_p$ does not admit a Schauder basis with constant one.

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On contractive projections in Hardy spaces

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