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.

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.

Obtaining a good similarity matrix is extremely important in subspace clustering. Current state-of-the-art methods learn the through self-expressive strategy. However, these directly adopt original samples as set of basis to represent itself linearly. It difficult accurately describe linear relation between real-world applications, and thus hard find an ideal matrix. To better samples, we prese...

Subspace clustering tries to find groups of similar objects from the given dataset such that the objects are projected on only a subset of the feature space. It finds meaningful clusters in all possible subspaces. However, when it comes to the quality of the resultant subspace clusters most of the subspace clusters are redundant. These redundant subspace clusters don’t provide new information. ...