On finite dimensional spaces, it is apparent that an operator is the product of two positive operators if and only if it is similar to a positive operator. Here, the class L+2 of bounded operators on separable infinite ...

It is widely recognized that UN peace operations have been critically influenced by their leadership personnel in the field since the first UN peacekeepers were deployed in 1948. But who exactly are the people that lead ...

Given a linear bounded selfadjoint operator a on a complex separable Hilbert space H, we study the decompositions of a as a difference of two positive operators whose ranges satisfy an angle condition. These decompositions ...

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 ...

Let A be a selfadjoint operator and P be an orthogonal projection both operating on a Hilbert space H. We say that A is P-complementable if A−µP≥ 0 holds for some µ ∈ R. In this case we define IP (A) = max{µ ∈ R : A − µP ...

This article is devoted to the study of the set T of all products PA with P an orthogonal projection and A a positive (semidefinite) operator. We describe this set and study optimal factorizations. We also relate this ...

Let A be a positive (semidefinite) bounded linear operator on a complex Hilbert space (H, ⟨ · , · ⟩). The semi-inner product induced by A is defined by ⟨ x, y⟩ A: = ⟨ Ax, y⟩ for all x, y∈ H and defines a seminorm ‖ · ‖ A ...