Groupoid Approach to Ergodic Dynamical System of Commutative von Neumann Algebra  

作　　者：Nicholas O. Okeke Murphy E. Egwe Nicholas O. Okeke;Murphy E. Egwe(Physical and Mathematical Sciences, Dominican University, Ibadan, Nigeria;Department of Mathematics, University of Ibadan, Ibadan, Nigeria)

机构地区：[1]Physical and Mathematical Sciences, Dominican University, Ibadan, Nigeria [2]Department of Mathematics, University of Ibadan, Ibadan, Nigeria

出　　处：《Advances in Pure Mathematics》2024年第3期167-184,共18页理论数学进展（英文）

摘　　要：Given a compact and regular Hausdorff measure space (X, μ), with μ a Radon measure, it is known that the generalised space M(X) of all the positive Radon measures on X is isomorphic to the space of essentially bounded functions L^∞(X, μ) on X. We confirm that the commutative von Neumann algebras M⊂B(H), with H=L²(X, μ), are unitary equivariant to the maximal ideals of the commutative algebra C(X). Subsequenly, we use the measure groupoid to formulate the algebraic and topological structures of the commutative algebra C(X) following its action on M(X) and define its representation and ergodic dynamical system on the commutative von Neumann algebras of M of B(H) .Given a compact and regular Hausdorff measure space (X, μ), with μ a Radon measure, it is known that the generalised space M(X) of all the positive Radon measures on X is isomorphic to the space of essentially bounded functions L^∞(X, μ) on X. We confirm that the commutative von Neumann algebras M⊂B(H), with H=L²(X, μ), are unitary equivariant to the maximal ideals of the commutative algebra C(X). Subsequenly, we use the measure groupoid to formulate the algebraic and topological structures of the commutative algebra C(X) following its action on M(X) and define its representation and ergodic dynamical system on the commutative von Neumann algebras of M of B(H) .

关 键 词：Measure Groupoid Groupoid Equivalence Ergodic Action Convolution Algebra von Neumann Algebra Generalized Space 

分 类 号：O15[理学—数学]