Spans and intersections of essentially reducing subspaces

Barycentric Subspaces and Affine Spans in Manifolds

This paper addresses the generalization of Principal Component Analysis (PCA) to Riemannian manifolds. Current methods like Principal Geodesic Analysis (PGA) and Geodesic PCA (GPCA) minimize the distance to a ”Geodesic subspace”. This allows to build sequences of nested subspaces which are consistent with a forward component analysis approach. However, these methods cannot be adapted to a backw...

Reducing subspaces

Let T be a self-adjoint operator acting in a separable Hilbert space H. We establish a correspondence between the reducing subspaces of T that come from a spectral projection and the convex, norm-closed bands in the set of finite Borel measures on R. IfH is not separable, we still obtain a reducing subspace corresponding to each convex norm-closed band. These observations lead to a unified trea...

On reducing and deflating subspaces of matrices

A multilinear approach based on Grassmann representatives and matrix compounds is presented for the identification of reducing pairs of subspaces that are common to two or more matrices. Similar methods are employed to characterize the deflating pairs of subspaces for a regular matrix pencil A+ sB, namely, pairs of subspaces (L,M) such that AL ⊆ M and BL ⊆ M.

Reducing Subspaces on the Annulus

We study reducing subspaces for an analytic multiplication operator Mzn on the Bergman space L 2 a(Ar) of the annulus Ar, and we prove that Mzn has exactly 2 reducing subspaces. Furthermore, in contrast to what happens for the disk, the same is true for the Hardy space on the annulus. Finally, we extend the results to certain bilateral weighted shifts, and interpret the results in the context o...

Inequalities for two systems of subspaces with prescribed intersections