# Unitary group orbits versus groupoid orbits of normal operators

@inproceedings{Belti2021UnitaryGO, title={Unitary group orbits versus groupoid orbits of normal operators}, author={Daniel Beltiţă and Gabriel Larotonda}, year={2021} }

We study the unitary orbit of a normal operator 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 differing 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 always has a natural manifold structure, modeled…

## References

SHOWING 1-10 OF 36 REFERENCES

### Unitary orbits of normal operators in von Neumann algebras

- Mathematics
- 2005

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…

### Linear algebraic groups in infinite dimensions

- Mathematics
- 1977

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…

### On the geometry of generalized inverses

- Mathematics
- 2005

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…

### The similarity orbit of a normal operator

- Mathematics
- 1975

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 ∗

- Mathematics
- 2008

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

- Mathematics
- 2001

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…

### A note on limits of unitarily equivalent operators

- Mathematics
- 1977

Let Qt(X) denote the set of all unitary operators on a separable complex Hilbert space SC. If T is a bounded linear operator on SC, let 'PT denote the mapping of qt(9C) onto qt(T) given by…