Infinite order decompositions of C$^*$-algebras

Details Infinite order decompositions of C$^*$-algebras Infinite order decompositions of C$^*$-algebras

2011-03-17

arxiv.org/abs/1103.3404v1

Mathematics

Operator Algebras

11 pages

Scientific paper

In the given article infinite order decompositions of C*-algebras are investigated. It is proved that for the infinite order decomposition of a C*-algebra A with respect to an infinite orthogonal set of projections of A, if the diagonal components of the infinite order decomposition are von Neumann algebras then the infinite order decomposition is a von Neumann algebra. Also, it is proved that, if a C*-algebra A with an infinite orthogonal set of projections such, that the least upper bound of this set is 1, is not a von Nemann algebra, projections of the set are pearwise equivalent then A does not coincide with its infinite order decomposition, and, if the infinite order decomposition is not weakly closed then this infinite order decomposition is not a C*-algebra.

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