paper

Operator Projective Line and Its Transformations

arXiv:2402.02595 · doi:10.1007/978-3-031-59397-0_12

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.

AMSLaTeX, 10 pages; v2: minor improvements; v3: minor improvements

Operator Projective Line and Its Transformations · wovepaper