Algebras of Gelfand-continuous functions into Arens-Michael algebras
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We characterize Gelfand-continuous functions from a Tychonoff space $X$ into an Arens-Michael algebra $A$. Then we define several algebras of such functions, and investigate them as topological algebras. Finally, we provide a class of examples of (metrizable) commutative unital complete Arens-Michael algebras $A$ and locally compact spaces $X$ for which all these algebras differ from each other.
Abstract
We characterize Gelfand-continuous functions from a Tychonoff space $X$ into an Arens-Michael algebra $A$. Then we define several algebras of such functions, and investigate them as topological algebras. Finally, we provide a class of examples of (metrizable) commutative unital complete Arens-Michael algebras $A$ and locally compact spaces $X$ for which all these algebras differ from each other.
참고문헌 (13)
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