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{\Large Department of Mathematics, BGU}

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{\Huge Operator Algebras Seminar}\\[0.2\baselineskip]

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\textbf{On} \emph{Wednesday, November 12, 2025}
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\textbf{At} \emph{13:00 -- 14:00}
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\textbf{In} \emph{201}

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{\large\scshape Ilan Hirshberg 
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  (BGU)
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will talk about
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{\Large\bfseries Isomorphisms between infinite free product C*-algebras\par}
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\textsc{Abstract:}
A \$C\^{}\textbackslash{}ast\$-probability space is a pair \$(A,\textbackslash{}tau)\$ consisting of a \$C\^{}\textbackslash{}ast\$-algebra and a tracial state \$\textbackslash{}tau\$ on \$A\$.
For any two \$C\^{}\textbackslash{}ast\$-probability spaces, there's a definition of a reduced free product \$C\^{}\textbackslash{}ast\$-algebra \$(A,\textbackslash{}tau) \textbackslash{}ast\_r (B,\textbackslash{}sigma)\$. 
This is a generalization of the case of reduced group \$C\^{}\textbackslash{}ast\$-algebras: if \$G\$ and \$H\$ are discrete groups, then the reduced free product of \$C\^{}\textbackslash{}ast\_r(G)\$ and \$C\^{}\textbackslash{}ast\_r(H)\$ is the reduced group \$C\^{}\textbackslash{}ast\$-algebra of the free product \$G \textbackslash{}ast H\$.
We show that if \$A\$ decomposes as a nontrivial reduced free power of infinitely many copies of separable \$C\^{}\textbackslash{}ast\$-probability spaces, then \$C({[}0,1{]}) \textbackslash{}ast\_r A\$ is isomorphic to \$A\$.
Several other related isomorphism theorems are obtained as well. I will review some background and outline the proof. 
This is joint work with N. Christopher Phillips.








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