比利时vs摩洛哥足彩
,
university of california san diego
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math 243: seminar in functional analysis
patrick hiatt
ucsd
a class of freely complemented masas in $l\mathbb{f}_n$
abstract:
i will present some recent joint work with nick boschert and ethan davis where we prove that if $a_1, a_2, \dots, a_n$ are abelian tracial w$^*$-algebras for $2\leq n \leq \infty$ and $m = a_1 * \cdots * a_n$ is their free product, then any subalgebra $\mathcal{a} \subset m$ of the form $\a = \sum_{i=1}^n u_i a_i p_i u_i^*$, for some projections $p_i \in a_i$ and unitaries $u_i \in \mathcal{u}(m)$, for $1 \leq i \leq n$, such that $\sum_i u_i p_i u_i^* = 1$, is freely complemented (fc) in $m$. we also show that any of the known maximal amenable masas $a\subset l\mathbb{f}_n$ satisfy popa's weak fc conjecture, namely there exists a haar unitary in $l\mathbb{f}_n$ that's free independent to $a$.
sri kunnawalkam elayavalli
december 3, 2024
11:00 am
apm b412
research areas
functional analysis / operator theory****************************
