带无条件基的Banach空间上正算子的不变子空间

Eva A. Gallardo-Guti'errez, Javier Gonz'alez-Dona, P. Tradacete
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引用次数: 0

摘要

证明了作用于Banach空间$\mathcal{X}$上的每个格同态具有一个非平凡闭不变子空间。事实上,它有一个非平凡的闭不变量理想,它不再对这样一个空间上的每一个正算子都成立。在这些例子的激励下,我们刻画了$\mathcal{X}$上没有非平凡闭不变量理想的三对角正算子,将Grivaux关于三对角算子非平凡闭不变量子空间存在性的结论推广到这一背景下。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Invariant subspaces for positive operators on Banach spaces with unconditional basis
We prove that every lattice homomorphism acting on a Banach space $\mathcal{X}$ with the lattice structure given by an unconditional basis has a non-trivial closed invariant subspace. In fact, it has a non-trivial closed invariant ideal, which is no longer true for every positive operator on such a space. Motivated by these later examples, we characterize tridiagonal positive operators without non-trivial closed invariant ideals on $\mathcal{X}$ extending to this context a result of Grivaux on the existence of non-trivial closed invariant subspaces for tridiagonal operators.
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