On contractive projections in Hardy spaces
  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. 
Florence Lancien (Universit\'e de Franche-Comt\'e, Besan\c{c}on,   France), Beata Randrianantoanina (Miami University, Oxfor...