Operator Projective Line and Its Transformations
Functional Analysis
2024-07-30 v3 Mathematical Physics
math.MP
Spectral Theory
Abstract
We introduce a concept of the operator (non-commutative) projective line PH defined by a Hilbert space H and a symplectic structure on it. Points of PH are Lagrangian subspaces of H. If a particular Lagrangian subspace is fixed then we can define SL(2,R)-action on PH. This gives a consistent framework for linear fractional transformations of operators. Some connections with spectral theory are outline as well.
Cite
@article{arxiv.2402.02595,
title = {Operator Projective Line and Its Transformations},
author = {Jafar Aljasem and Vladimir V. Kisil},
journal= {arXiv preprint arXiv:2402.02595},
year = {2024}
}
Comments
AMSLaTeX, 10 pages; v2: minor improvements; v3: minor improvements