Author

A. Acuaviva

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Preprint Sep 2026

A negative solution to the complemented subspace problem for Banach spaces with unconditional bases

We give a negative solution to the complemented subspace problem for Banach spaces with unconditional bases over both the real and complex fields. For every $\rho>0$, we construct a projection $P_\rho$ of norm less than $1+\rho$ on a separable superreflexive space \begin{equation*} X_\rho=\left(\bigoplus_{j=1}^{\infty}...

A. Acuaviva · 0 citations

Preprint Aug 2026

CNOT-Distance is NP-complete under all-to-all connectivity

A polynomial-time decoder yields NP-hardness of approximation within every fixed additive constant and, through an L-reduction from Minimum Vertex Cover on cubic graphs, APX-hardness of the associated CNOT-circuit optimisation problem.

A. Acuaviva, Arturo Acuaviva, Pablo Acuaviva · 2 citations