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Muhly, P.S., Renault, J.N. and Williams, D.P. (1987) Equivalence and Isomorphism for Groupoid C*-Algebras. Journal of Operator Theory, 17, 3-22.

has been cited by the following article:

• TITLE: Groupoid Approach to Ergodic Dynamical System of Commutative von Neumann Algebra

  AUTHORS: Nicholas O. Okeke, Murphy E. Egwe

  KEYWORDS: Measure Groupoid, Groupoid Equivalence, Ergodic Action, Convolution Algebra, von Neumann Algebra, Generalized Space

  JOURNAL NAME: Advances in Pure Mathematics, Vol.14 No.3, March 26, 2024

  ABSTRACT: 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) .