Let $\{τ_j\}_{j=1}^n$ and $\{ω_k\}_{k=1}^n$ be two orthonormal bases for a finite dimensional p-adic Hilbert space $\mathcal{X}$. Let $M,N\subseteq \{1, \dots, n\}$ be such that \begin{align*} \displaystyle \max_{j \in M, k \in N}|\langle τ_j, ω_k \rangle|<1, \end{align*} where $o(M)$ is the cardinality of $M$. Then for all $x \in \mathcal{X}$, we show that \begin{align} (1) \quad \quad \quad \quad \|x\|\leq \left(\frac{1}{1-\displaystyle \max_{j \in M, k \in N}|\langle τ_j, ω_k \rangle|}\right)\max\left\{\displaystyle \max_{j \in M^c}|\langle x, τ_j\rangle |, \displaystyle \max_{k \in N^c}|\langle x, ω_k\rangle |\right\}. \end{align} We call Inequality (1) as \textbf{p-adic Ghobber-Jaming Uncertainty Principle}. Inequality (1) is the p-adic version of uncertainty principle obtained by Ghobber and Jaming \textit{[Linear Algebra Appl., 2011]}. We also derive analogues of Inequality (1) for non-Archimedean Banach spaces.

翻译：设 $\{τ_j\}_{j=1}^n$ 和 $\{ω_k\}_{k=1}^n$ 是有限维 p-adic Hilbert 空间 $\mathcal{X}$ 上的两组标准正交基。令 $M,N\subseteq \{1, \dots, n\}$ 满足条件 \begin{align*} \displaystyle \max_{j \in M, k \in N}|\langle τ_j, ω_k \rangle|<1, \end{align*} 其中 $o(M)$ 表示 $M$ 的基数。那么对于所有 $x \in \mathcal{X}$，我们证明有 \begin{align} (1) \quad \quad \quad \quad \|x\|\leq \left(\frac{1}{1-\displaystyle \max_{j \in M, k \in N}|\langle τ_j, ω_k \rangle|}\right)\max\left\{\displaystyle \max_{j \in M^c}|\langle x, τ_j\rangle |, \displaystyle \max_{k \in N^c}|\langle x, ω_k\rangle |\right\}. \end{align} 我们称不等式 (1) 为 \textbf{p-adic Ghobber-Jaming 不确定性原理}。不等式 (1) 是 Ghobber 和 Jaming 在文献 \textit{[Linear Algebra Appl., 2011]} 中所得不确定性原理的 p-adic 版本。我们还推导了不等式 (1) 在非阿基米德 Banach 空间中的类似形式。