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A $C^*$-algebraic Schoenberg theorem

A $C^*$-algebraic Schoenberg theorem

Let ๐”„ be a C * -algebra, G a compact abelian group, ฯ„ an action of G by *-automorphisms of ๐”„,๐”„ ฯ„ the fixed point algebra of ฯ„ and ๐”„ F the dense sub-algebra of G-finite elements in ๐”„. Further let H be a linear operator from ๐”„ F into โ€ฆ