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Classification of Nuclear C*-Algebras. Entropy in Operator Algebras (Paperback, Softcover reprint of hardcover 1st ed. 2002)
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Classification of Nuclear C*-Algebras. Entropy in Operator Algebras (Paperback, Softcover reprint of hardcover 1st ed. 2002)
Series: Encyclopaedia of Mathematical Sciences, 126
Expected to ship within 10 - 15 working days
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to the Encyclopaedia Subseries on Operator Algebras and
Non-Commutative Geometry The theory of von Neumann algebras was
initiated in a series of papers by Murray and von Neumann in the
1930's and 1940's. A von Neumann algebra is a self-adjoint unital
subalgebra M of the algebra of bounded operators of a Hilbert space
which is closed in the weak operator topology. According to von
Neumann's bicommutant theorem, M is closed in the weak operator
topology if and only if it is equal to the commutant of its
commutant. Afactor is a von Neumann algebra with trivial centre and
the work of Murray and von Neumann contained a reduction of all von
Neumann algebras to factors and a classification of factors into
types I, II and III. C* -algebras are self-adjoint operator
algebras on Hilbert space which are closed in the norm topology.
Their study was begun in the work of Gelfand and Naimark who showed
that such algebras can be characterized abstractly as involutive
Banach algebras, satisfying an algebraic relation connecting the
norm and the involution. They also obtained the fundamental result
that a commutative unital C* -algebra is isomorphic to the algebra
of complex valued continuous functions on a compact space - its
spectrum. Since then the subject of operator algebras has evolved
into a huge mathematical endeavour interacting with almost every
branch of mathematics and several areas of theoretical physics.
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