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Department of Mathematics,
Department of Mathematics,
University of California San Diego
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Math 243: Seminar in Functional Analysis
Junchen Zhao
Texas A&M University
Free products and rescalings involving non-separable abelian von Neumann algebras
Abstract:
For a self-symmetric tracial von Neumann algebra $A$, we study rescalings of $A^{*n}*L\mathbb F_r$ for $n\in\mathbb N$ and $r\in (1,\infty]$ and use them to obtain an interpolation $\mathcal F_{s,r}(A)$ for all real numbers $s > $0 and $1 − s < r \leq\infty$. In this talk, I will first review the literature around this topic and explain well-definedness of the family $\mathcal F_{s,r}(A)$. I will discuss our definition of self-symmetry which includes all diffuse abelian tracial von Neumann algebras regardless of separability, and then focus on free products of infinitely many members of the family $\mathcal F_{s,r}(A_i)$. This is joint work with Ken Dykema.
January 6, 2026
11:00 AM
APM 6402
Research Areas
Functional Analysis / Operator Theory****************************
