Unitary Group Orbits Versus Groupoid Orbits of Normal Operators

@article{Belti2021UnitaryGO,
  title={Unitary Group Orbits Versus Groupoid Orbits of Normal Operators},
  author={Daniel Beltiţă and Gabriel Larotonda},
  journal={The Journal of Geometric Analysis},
  year={2021},
  volume={33},
  pages={1-44}
}
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… 

References

SHOWING 1-10 OF 46 REFERENCES

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