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arXiv · 2402.02595

Operator Projective Line and Its Transformations

Jafar Aljasem·Vladimir V. Kisil
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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.

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Jafar Aljasem, Vladimir V. Kisil. 2024-02-04. Operator Projective Line and Its Transformations. https://doi.org/10.1007/978-3-031-59397-0_12

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