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arXiv · 2609.01447

Kazhdan's Property $(T)$ for Subspaces and Quotients of $L_p$-Spaces

Qingjin Cheng
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Abstract

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 $1<p<\infty$.

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Qingjin Cheng. 2026-09-01. Kazhdan's Property $(T)$ for Subspaces and Quotients of $L_p$-Spaces. https://arxiv.org/abs/2609.01447

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