Unitary Group Orbits Versus Groupoid Orbits of Normal Operators

  title={Unitary Group Orbits Versus Groupoid Orbits of Normal Operators},
  author={Daniel Beltiţă and Gabriel Larotonda},
  journal={The Journal of Geometric Analysis},
We study the unitary orbit of a normal operator $$a\in {{\mathcal {B}}}({{\mathcal {H}}})$$ a ∈ B ( H ) , regarded as a homogeneous space for the action of unitary groups associated with symmetrically normed ideals of compact operators. We show with an unified treatment that the orbit is a submanifold of the various ambient spaces if and only if the spectrum of a is finite, and in that case, it is a closed submanifold. For arithmetically mean closed ideals, we show that nevertheless the orbit… 



Unitary orbits of normal operators in von Neumann algebras

Abstract The starting points for this paper are simple descriptions of the norm and strong* closures of the unitary orbit of a normal operator in a von Neumann algebra. The statements are in terms of

Geometry of unitary orbits of pinching operators

On the geometry of generalized inverses

We study the set S = {(a, b) ∈ A × A : aba = a, bab = b} which pairs the relatively regular elements of a Banach algebra A with their pseudoinverses, and prove that it is an analytic submanifold of A

Linear algebraic groups in infinite dimensions

An important fact in the finite dimensional theory of Lie groups is that every closed subgroup of a Lie group is itself a Lie group. However, this is not always the case in infinite dimensions. In

The similarity orbit of a normal operator

If N is a bounded normal operator on a separable Hilbert space H, let S(N) denote the similarity orbit of N in L(H) and let Sk(N) denote the set of all compact perturbations of elements of S(N). It

Finsler geometry and actions of the p-Schatten unitary groups ∗

Let p be an even positive integer and U p (H) the Banach-Lie group of unitary operators u which verify that u — 1 belongs to the p-Schatten ideal B p (H). Let O be a smooth manifold on which U p (H)

Infinite-dimensional Groups and their Representations

This article provides an introduction to the representation theory of Banach-Lie groups of operators on Hilbert spaces, where our main focus lies on highest weight representations and their geometric

Poisson geometrical aspects of the Tomita-Takesaki modular theory

We investigate some genuine Poisson geometric objects in the modular theory of an arbitrary von Neumann algebra $\mathfrak{M}$. Specifically, for any standard form realization