Year: 2026
Type: preprint
Abstract: For every von Neumann algebra \(\M\), we prove that each bounded sequence in the Haagerup space \(L_1(\M)=\M_*\) admits either a norm-convergent subsequence or a \(2\)-co-lacunary subsequence. This answers an open problem of Parcet and Randrianantoanina \cite[Remark~3.11]{ParcetRandrianantoanina2006} and removes both hyperfiniteness and semifiniteness.
Source: arXiv (Cornell University)
Authors: Huang, Jinghao, Zhu, Yunpeng
Institution: Harbin Institute of Technology
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7221807219