论文标题
统一的兼容性理论方法的方法可逆插值操作员
A unified approach to compatibility theorems on invertible interpolated operators
论文作者
论文摘要
We prove the stability of isomorphisms between Banach spaces generated by interpolation methods introduced by Cwikel-Kalton-Milman-Rochberg which includes, as special cases, the real and complex methods up to equivalence of norms and also the so-called $\pm$ or $G_1$ and $G_2$ methods defined by Peetre and Gustavsson-Peetre.该结果用于显示某些操作员分析方程的解决方案的存在。这些结果的a是Albrecht-Müller结果的更一般变体，该变体指出，插值同构可以满足插值空间之间的独特性。我们展示了Calderón功能晶格之间的正运算符的应用。我们还得出了插值操作员光谱之间的连接。
We prove the stability of isomorphisms between Banach spaces generated by interpolation methods introduced by Cwikel-Kalton-Milman-Rochberg which includes, as special cases, the real and complex methods up to equivalence of norms and also the so-called $\pm$ or $G_1$ and $G_2$ methods defined by Peetre and Gustavsson-Peetre. This result is used to show the existence of solution of certain operator analytic equation. A by product of these results is a more general variant of the Albrecht-Müller result which states that the interpolated isomorphisms satisfy uniqueness-of-inverses between interpolation spaces. We show applications for positive operators between Calderón function lattices. We also derive connections between the spectrum of interpolated operators.
