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- W2982307054 abstract "In 1970, Chou showed there are $|mathbb{N}^*| = 2^{2^mathbb{N}}$ topologically invariant means on $L_infty(G)$ for any noncompact, $sigma$-compact amenable group. Over following 25 years, sizes of sets of topologically invariant means on $L_infty(G)$ and $VN(G)$ were determined for any locally compact group. Each paper on a new case reached same conclusion -- the cardinality is as large as possible -- but a unified proof never emerged. In this paper, I show $L_1(G)$ and $A(G)$ always contain orthogonal nets converging to invariance. An orthogonal net indexed by $Gamma$ has $|Gamma^*|$ accumulation points, where $|Gamma^*|$ is determined by ultrafilter theory. Among a smattering of other results, I prove Paterson's conjecture that left and right topologically invariant means on $L_infty(G)$ coincide iff $G$ has precompact conjugacy classes." @default.
- W2982307054 created "2019-11-08" @default.
- W2982307054 creator A5091343946 @default.
- W2982307054 date "2019-06-24" @default.
- W2982307054 modified "2023-09-27" @default.
- W2982307054 title "Counting topologically invariant means on $L_infty(G)$ and $VN(G)$ with ultrafilters" @default.
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