Averaging projections for the canonical basis are uniformly bounded in weighted Lorentz sequence spaces ℓ_{p,q} (0<q<1<p<∞), showing this property does not characterize local convexity among quasi-Banach spaces with symmetric bases.
Aoki,Locally bounded linear topological spaces, Proc
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Boundedness of the averaging projections in nonlocally convex Lorentz sequence spaces and applications to basis theory
Averaging projections for the canonical basis are uniformly bounded in weighted Lorentz sequence spaces ℓ_{p,q} (0<q<1<p<∞), showing this property does not characterize local convexity among quasi-Banach spaces with symmetric bases.