论文标题
无条件的Banach空间上正面运营商的不变子空间
Invariant subspaces for positive operators on Banach spaces with unconditional basis
论文作者
论文摘要
我们证明，用无条件的基础给出的晶格结构都具有非平凡的封闭不变子空间。实际上，它具有非平凡的封闭不变理想，对于这样一个空间上的每个积极操作员来说，这是不再如此。在以后的示例中，我们表征了tridiagonal正算子，而没有非平凡的封闭不变的理想，这是$ \ Mathcal {x} $扩展到此上下文的结果，这是Grivaux对Tridiagonal Operator的非平凡封闭不变子空间的结果。
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.
