AI 中文总结
该研究证明了L^p空间上个体最终正C0半群的增长界与其生成元的谱界一致，通过适配算子范围均匀化原理完成证明，解答了Vogt提出的相关问题。
AI 中文摘要
我们通过证明L^p空间（1 < p < ∞）上的个体最终正C0半群的增长界与其生成元的谱界一致，回答了Vogt提出的问题。我们的证明遵循Vogt针对一致最终正情形的论证的总体策略，关键新要素是Arora与Glück提出的算子范围均匀化原理的变体，此处适配于随时间变化的算子范围。当应用于主理想时，该原理将个体最终正性转化为Vogt稳定性论证所需的一致控制估计。
英文摘要
We answer a question raised by Vogt by proving that the growth bound of an individually eventually positive $C_0$-semigroup on an $L^p$-space ($1 < p < \infty$) coincides with the spectral bound of its generator. Our proof follows the general strategy of Vogt's argument for the uniformly eventually positive case. The key new ingredient is a variant of an operator-range uniformisation principle of Arora and Glück, adapted here to time-dependent operator ranges. When applied to principal ideals, this principle turns individual eventual positivity into the uniform domination estimate required for Vogt's stability argument.
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