Tag: Gelfand duality

• Motivating Noncommutative Geometry: Gelfand Duality and the Slogan 'Space = Algebra of Functions'We prove the Gelfand–Naimark theorem matching commutative C*-algebras with locally compact spaces, then motivate noncommutative spaces via quantum commutators and bad quotients.MathematicsNoncommutative GeometryResearchC*-algebrasGelfand dualityoperator algebrasnoncommutative torus~34 min