C*-Algebra Relations

Details C*-Algebra Relations C*-Algebra Relations

2008-07-31

arxiv.org/abs/0807.4988v3

Math. Scand. 107 (2010), no. 1, 43-72

Mathematics

Operator Algebras

Added a few examples. 24 pages

Scientific paper

We investigate relations on elements in C*-algebras, including *-polynomial relations, order relations and all relations that correspond to universal C*-algebras. We call these C*-relations and define them axiomatically. Within these are the compact C*-relations, which are those that determine universal C*-algebras, and we introduce the more flexible concept of a closed C*-relation. In the case of a finite set of generators, we show that closed C*-relations correspond to the zero-sets of elements in a free sigma -C*-algebra. This provides a solid link between two of the previous theories on relations in C*-algebras. Applications to lifting problems are briefly considered in the last section.

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