Tag: operator algebras

• C*-Algebras: Spectral Theory and the Gelfand RepresentationSpectra in Banach algebras are nonempty and compact; from this we derive the spectral radius formula, identify commutative C*-algebras with C0(X), and build the functional calculus.MathematicsNoncommutative GeometryResearchoperator algebrasC*-algebrasspectral theoryGelfand representation~37 min
• 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