论文标题
Quasinilpotent运算符的ISP的有条件证明
A conditional proof of the ISP for quasinilpotent operators
论文作者
论文摘要
不变的子空间问题（ISP）是功能分析中众所周知的未解决问题。尽管已知许多部分结果，但复杂的无限尺寸可分离希尔伯特空间的一般情况仍然开放。已经表明，可以将问题简化为运算符的情况，这是尼尔植物的规范限制。最重要的子案例之一是Quasinilpotent操作员之一，为此，该问题已被广泛研究了很多年。在本文中，我们将引入一个新的猜想（在启发式论点的支持下），我们将有条件地证明，每个Quasinilpotent操作员都有一个非平凡的不变子空间。我们将提出一个开放问题，这将对ISP产生深远的影响。
The invariant subspace problem (ISP) is a well known unsolved problem in funtional analysis. While many partial results are known, the general case for complex, infinite dimensional separable Hilbert spaces is still open. It has been shown that the problem can be reduced to the case of operators which are norm limits of nilpotents. One of the most important subcases is the one of quasinilpotent operators, for which the problem has been extensively studied for many years. In this paper, we will introduce a new conjecture (supported by a heuristic argument), and we will prove conditionally that every quasinilpotent operator has a nontrivial invariant subspace. We will conclude by posing an open problem which would have deep implications regarding the ISP.
