# 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…

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