Abstract

In year 2006 the author proposed an approach to the invariant subspace problem for an operator on a Hilbert space, based on projection-convex combinations in \(C^{*}\)-algebras with the unitary factorization property. In this paper, we present an operator inequality characterizing the invariant subspace of such an operator. Eight corollaries are obtained. For an operator \(C^{*}\)-algebra \(\mathcal{A}\) with a faithful trace, we give a sufficient condition of commutation for a partial isometry from \(\mathcal{A}\) with a projection onto its invariant subspace.

中文翻译：

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希尔伯特空间上算子的不变子空间

摘要

2006年，作者基于具有\因式分解性质的\（C ^ {*} \）-代数中的投影-凸组合，为希尔伯特空间上的算子提出了不变子空间问题的方法。在本文中，我们提出了一个算子不等式，刻画了该算子的不变子空间。获得八个推论。对于操作者\（C ^ {*} \） -代数\（\ mathcal {A} \）与忠实迹，我们给换向的一个充分条件，用于从部分等距\（\ mathcal {A} \）与在其不变子空间上的投影。