关于算子非紧性测度的多线性扎弗兰定理
A multilinear Zafran theorem for the measure of noncompactness of operators
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中文总结 AI 辅助
研究作用于拟巴拿赫空间乘积上算子的多线性扎弗兰定理，通过考虑拟巴拿赫对间多线性算子，依序列空间基本函数获插值估计，还研究插值多线性算子非紧性测度，得出结果并扩展了相关早期结论。
中文摘要 AI 辅助
我们建立了扎弗兰插值定理的多线性类似物，用于作用在由一般实方法生成的拟巴拿赫空间乘积上的算子。我们考虑拟巴拿赫对之间的多线性算子，并根据基础序列空间的基本函数获得插值估计。作为应用，我们研究了在此设置下插值多线性算子的非紧性测度，并得出该量的相应插值估计。特别是，我们得到了作用在与抽象实方法相关空间上的插值多线性算子的单侧紧性结果。这些结果将已知的双线性定理作为特殊情况恢复，并扩展了关于多线性插值和非紧性测度插值的早期结果。
英文摘要
We establish a multilinear analogue of Zafran's interpolation theorem for operators acting on products of quasi-Banach spaces generated by the general real methods. We consider multilinear operators between quasi-Banach couples and obtain interpolation estimates expressed in terms of the fundamental functions of the underlying sequence spaces. As an application, we study the measure of noncompactness of interpolated multilinear operators in this setting and derive a corresponding interpolation estimate for this quantity. In particular, we obtain a one-sided compactness result for interpolated multilinear operators acting on spaces associated with the abstract real methods. These results recover known bilinear theorems as special cases and extend earlier results on multilinear interpolation and on the interpolation of the measure of noncompactness.
