Non Commutative Topology and Local Structure of Operator Algebras

Details Non Commutative Topology and Local Structure of Operator Algebras Non Commutative Topology and Local Structure of Operator Algebras

2002-05-23

arxiv.org/abs/math/0205257v1

Mathematics

Operator Algebras

23 pages

Scientific paper

Starting with a $W^{*}$-algebra $M$ we use the inverse system obtained by cutting down $M$ by its (central) projections to define an inverse limit of $W^{*}$-algebras, and show that how this pro-$W^{*}$-algebra encodes the local structure of $M$. For the $C^{*}$-algebras we do the same thing using their atomic enveloping $W^{*}$-algebra . We investigate the relation of these ideas to the Akemann-Giles-Kummer non commutative topology. Finally we use these ideas to look at the local structure of Kac algebras.

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