Noncommutative weak almost periodicity and left uniform continuity over locally compact quantum groups
Abstract
We study weak almost periodicity and left uniform continuity for Hopf-von Neumann algebras and locally compact quantum groups. For a Hopf-von Neumann algebra (M,Γ), we introduce the space WAPBessel,πu(M*) through norm convergence conditions on rows and columns of slices associated with Bessel families in the universal representation. We prove that this space is the largest C*-subalgebra of WAP(M*) when separately continuous lift of the co-multiplication is multiplicative, and that the two spaces coincide when M is commutative. Furthermore, the algebra {x∈ Cb(𝔾): Γ(x)∈ M(C0(𝔾)⊗ Cb(𝔾))} is characterized as the greatest left introverted C*-subalgebra of LUC(L1(𝔾)) satisfying a left Bessel condition on L2(𝔾). We also show that LUC(L1(𝔾)) is a C*-algebra whenever the center of C0(𝔾) contains an element on which the bounded counit is non-zero.
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BibTeX
@misc{faal2026noncommutative,
title = {{Noncommutative weak almost periodicity and left uniform continuity over locally compact quantum groups}},
author = {Ramin Faal and Amin Allah Khosravi and Hamid Reza Ebrahimi Vishki},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.07168},
eprint = {2611.07168},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.07168},
}
RIS
TY - UNPB
TI - Noncommutative weak almost periodicity and left uniform continuity over locally compact quantum groups
AU - Ramin Faal
AU - Amin Allah Khosravi
AU - Hamid Reza Ebrahimi Vishki
PY - 2026
DA - 2026/11/04
PB - arXiv
DO - 10.48550/arxiv.2611.07168
UR - https://arxiv.org/abs/2611.07168
AB - We study weak almost periodicity and left uniform continuity for Hopf-von Neumann algebras and locally compact quantum groups. For a Hopf-von Neumann algebra (M,Γ), we introduce the space WAP_Bessel,π_u(M_*) through norm convergence conditions on rows and columns of slices associated with Bessel families in the universal representation. We prove that this space is the largest C^*-subalgebra of WAP(M_*) when separately continuous lift of the co-multiplication is multiplicative, and that the two spaces coincide when M is commutative. Furthermore, the algebra {x∈ C_b(𝔾): Γ(x)∈ M(C_0(𝔾)⊗ C_b(𝔾))} is characterized as the greatest left introverted C^*-subalgebra of LUC(L^1(𝔾)) satisfying a left Bessel condition on L^2(𝔾). We also show that LUC(L^1(𝔾)) is a C^*-algebra whenever the center of C_0(𝔾) contains an element on which the bounded counit is non-zero.
ER -