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A thorough account of the methods that underlie the theory of subalgebras of finite von Neumann algebras, this book contains a substantial amount of current research material and is ideal for those studying operator algebras. The conditional expectation, basic construction and perturbations within a finite von Neumann algebra with a fixed faithful normal trace are discussed in detail. The general theory of maximal abelian self-adjoint subalgebras (masas) of separable II1 factors is presented with illustrative examples derived from group von Neumann algebras. The theory of singular masas and Sorin Popa's methods of constructing singular and semi-regular masas in general separable II1 factor are explored. Appendices cover the ultrapower of a II1 factor and the properties of unbounded operators required for perturbation results. Proofs are given in considerable detail and standard basic examples are provided, making the book understandable to postgraduates with basic knowledge of von Neumann algebra theory.

Von Neumann algebras --- Algebras, Von Neumann --- Algebras, W --- Neumann algebras --- Rings of operators --- W*-algebras --- C*-algebras --- Hilbert space --- Von Neumann algebras.

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Functional analysis --- 51 --- Von Neumann algebras --- Factors (Algebra) --- Algebra --- Factorization (Mathematics) --- Algebras, Von Neumann --- Algebras, W --- Neumann algebras --- Rings of operators --- W*-algebras --- C*-algebras --- Hilbert space --- Mathematics --- Von Neumann algebras. --- Factors (Algebra). --- 51 Mathematics

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Analytical spaces --- 517.986 --- Von Neumann algebras --- Algebras, Von Neumann --- Algebras, W --- Neumann algebras --- Rings of operators --- W*-algebras --- C*-algebras --- Hilbert space --- Topological algebras. Theory of infinite-dimensional representations --- Von Neumann algebras. --- 517.986 Topological algebras. Theory of infinite-dimensional representations --- Algèbres topologiques --- Topological algebras --- Algèbres topologiques. --- Topological algebras. --- Algebres topologiques --- Algebres de von neumann

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Analytical spaces --- Ergodentheorie --- Ergodic theory --- Ergodique [Theorie ] --- Limiettheorema's (Waarschijnlijkheidstheorie) --- Limit theorems (Probability theory) --- Théorèmes limites (Théorie des probabilités) --- Von Neumann [Algebra's van ] --- Von Neumann [Algèbres de ] --- Von Neumann algebras --- 51 --- Algebras, Von Neumann --- Algebras, W --- Neumann algebras --- Rings of operators --- W*-algebras --- C*-algebras --- Hilbert space --- Probabilities --- Ergodic transformations --- Continuous groups --- Mathematical physics --- Measure theory --- Transformations (Mathematics) --- Mathematics --- 51 Mathematics

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Analytical spaces --- 517.986 --- Von Neumann algebras --- Algebras, Von Neumann --- Algebras, W --- Neumann algebras --- Rings of operators --- W*-algebras --- C*-algebras --- Hilbert space --- Topological algebras. Theory of infinite-dimensional representations --- Von Neumann algebras. --- 517.986 Topological algebras. Theory of infinite-dimensional representations --- Algebres topologiques --- Algebres de von neumann