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Bibliographic Details
Main Authors: Aljasem, Jafar, Kisil, Vladimir V.
Format: Preprint
Published: 2024
Subjects:
Online Access:https://arxiv.org/abs/2402.02595
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author Aljasem, Jafar
Kisil, Vladimir V.
author_facet Aljasem, Jafar
Kisil, Vladimir V.
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2402_02595
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Operator Projective Line and Its Transformations
Aljasem, Jafar
Kisil, Vladimir V.
Functional Analysis
Mathematical Physics
Spectral Theory
46C05, 47A11, 53D05, 81S10
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.
title Operator Projective Line and Its Transformations
topic Functional Analysis
Mathematical Physics
Spectral Theory
46C05, 47A11, 53D05, 81S10
url https://arxiv.org/abs/2402.02595