C-algebra relations
- Autores: Terry A. Loring
- Localización: Mathematica scandinavica, ISSN 0025-5521, Vol. 107, Nº 1, 2010, págs. 43-72
- Idioma: inglés
- Enlaces
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Resumen
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 σ-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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