Some results concerning hyperinvariant subspaces of some operators on locally convex spaces are considered. Denseness of a class of operators which have a hyperinvariant subspace in the algebra of locally bounded operators is proved.

It is proved that in order to find a nontrivial hyperinvariant subspace for a cohyponormal operator it suffices to make the further assumption that the operator have the single-valued extension property.

The search for exoplanets is pushing adaptive optics (AO) systems on ground-based telescopes to their limits. One of the major limitations at small angular separations, exactly where are predicted be, servo-lag AO systems. error can be reduced with predictive control based future state atmospheric disturbance. We propose use a linear data-driven integral controller subspace methods that updated...

We define a new notion of affine subspace concentration conditions for lattice polytopes, and prove that they hold smooth reflexive polytopes with barycenter at the origin. Our proof involves considering slope stability canonical extension tangent bundle by trivial line class $c_1(\mathcal{T}_X)$ on Fano toric varieties.