Abstract theory of Abelian operator algebras: an application of forcing. (English) Zbl 0597.03030
The author develops a new abstract Abelian operator theory which may be understood as a generalization of Stone’s axiomatic theory of Abelian algebras of bounded operators. He introduces axiomatically algebraic structures which are called Stonean algebras. These are essentially normed commutative algebras with involution, where however the norm does not necessarily take only finite values. The author’s theory is a clever application of the Scott-Solovay-Vopenka method of Boolean-valued models of set theory.
Reviewer: U.Felgner
MSC:
| 03E40 | Other aspects of forcing and Boolean-valued models |
| 46J25 | Representations of commutative topological algebras |
| 03E75 | Applications of set theory |
Keywords:
representations of Stonean algebras; commutative topological; algebras; normed commutative algebras with involution; Boolean-valued modelsReferences:
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