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Kazhdan's Property (T) for Subspaces and Quotients of Lp-Spaces
Abstract
We prove a uniform spectral-gap estimate at every even exponent for isometric representations on arbitrary closed subspaces of real Lp-spaces. As an application, this result, combined with the work of Bader, Furman, Gelander and Monod, gives an affirmative answer to their Question 4.1: Kazhdan's property (T) implies property (TX) whenever X is a closed subspace or a quotient of a real Lp-space, for every 1<p<∞.
Related
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BibTeX
@misc{cheng2026kazhdans,
title = {{Kazhdan's Property $(T)$ for Subspaces and Quotients of $L_p$-Spaces}},
author = {Qingjin Cheng},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.01447},
eprint = {2609.01447},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.01447},
}
RIS
TY - UNPB
TI - Kazhdan's Property (T) for Subspaces and Quotients of L_p-Spaces
AU - Qingjin Cheng
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.01447
UR - https://arxiv.org/abs/2609.01447
AB - We prove a uniform spectral-gap estimate at every even exponent for isometric representations on arbitrary closed subspaces of real L_p-spaces. As an application, this result, combined with the work of Bader, Furman, Gelander and Monod, gives an affirmative answer to their Question 4.1: Kazhdan's property (T) implies property (T_X) whenever X is a closed subspace or a quotient of a real L_p-space, for every 1<p<∞.
ER -