A riemannian metric is introduced in the infinite dimensional manifold Σ_n of positive operators with rank n<∞ on a Hilbert space H.  The geometry of this manifold is studied and related to the geometry of the submanifolds ...

We investigate the behavior of finitely generated projective modules over a down-up algebra. Specifically, we show that every noetherian down-up algebra A(α,β,γ) has a non-free, stably free right ideal. Further, we compute ...

Let H = H+ ⊕ H− be a fixed orthogonal decomposition of a Hilbert space, with both subspaces of infinite dimension, and let E+, E− be the projections onto H+ and H−. We study the set Pcc of orthogonal projections P in H ...

Let H= H+⊕ H- be a fixed orthogonal decomposition of the complex separable Hilbert space H in two infinite-dimensional subspaces. We study the geometry of the set Pp of selfadjoint projections in the Banach algebra Ap= { ...

Many rings and algebras arising in quantum mechanics, algebraic analysis, and non-commutative algebraic geometry can be interpreted as skew PBW (Poincare- Birkhoff Witt) extensions. In the present paper we study two aspects ...

We study the set C consisting of pairs of orthogonal projectionsP,Q acting in a Hilbert space H such that PQ is a compact operator. Thesepairs have a rich geometric structure which we describe here. They are partitionedin ...

Let K be a complete infinite rank valued field, In [4] we studied Norm Hilbert Spaces (NHS) over K i.e, K-Banach spaces for which closed subspaces admit projections of norm less than or equal to 1. In this paper we prove ...