Geodesic neighborhoods in unitary orbits of self-adjoint operators of K+C

Tamara Bottazzi; Alejandro Varela

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arXiv · 1904.03650

Geodesic neighborhoods in unitary orbits of self-adjoint operators of K+C

Tamara Bottazzi·Alejandro Varela

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Abstract

We study the unitary orbit of a compact Hermitian diagonal operator with spectral multiplicity one under the action of the unitary group U_(K+C) of the unitization of the compact operators K(H)+C, or equivalently, the quotient U_(K+C)/ U_Diag(K+C). We relate this and the action of different unitary subgroups to describe metric geodesics (using a natural distance) which join end points. As a consequence we obtain a local Hopf-Rinow theorem. We also explore cases about the uniqueness of short curves and prove that there exist some of these that cannot be parameterized using minimal anti-Hermitian operators of K(H)+C.

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BibTeX RIS

Tamara Bottazzi, Alejandro Varela. 2019-04-07. Geodesic neighborhoods in unitary orbits of self-adjoint operators of K+C. https://arxiv.org/abs/1904.03650

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