代数K理论中的极分解

由极式分解的分支生成的C* 代数的结构

On the structure of C*-algebras generated by the components of polar decompositions

本文研究了希尔伯特空间中满足一定对易关系的算子的极式分解的分支所生成的C^*-代数的结构。

C*代数中元素到正规元素的距离与极分解

Distance to regular elements and polar decompositions in a C*-algebra

本文研究了C*代数中元素到正规元素的距离，通过极分解的截断部分来确定该距离，并与已有关于可逆和准可逆元素距离的结果形成对比。

The polar decomposition for adjointable operators on Hilbert $C^*$-modules and centered operators

Let $T$ be an adjointable operator between two Hilbert $C^*$-modules and $T^*$ be the adjoint operator of $T$. The polar decomposition of $T$ is characterized as $T=U(T^*T)^\frac12$ and $\mathcal{R}(U^*)=\overline{\mathcal{R}(T^*)}$, where $U$ is a partial isometry, $\mathcal{R}(U^*)$ and $\overline{\mathcal{R}(T^*)}$ denote the range of $U^*$ and the norm closure of the range of $T^*$, respectively. Based on this new characterization of the polar decomposition, an application to the study of centered operators is carried out.

三个算子乘积的极分解

The polar decomposition of the product of three operators

本文在Hilbert $C^*$-模上研究三个算子乘积的极分解，阐明其相互关系，并给出乘法扰动极分解公式及相关刻画。

AW *-代数的谱分解和极分解

Spectral and polar decomposition in AW*-algebras

证明了任意AW*-代数的元素在其内部极分解的可能性和唯一性。证明了正规AW*-代数的正规元的谱分解是可能的，且在正规AW*-代数内部是唯一的。正规元谱分解的可能性不依赖于AW*-代数的正规性。

New multiplicative perturbation bounds for the generalized polar decomposition

Some new Frobenius norm bounds of the unique solution to certain structured Sylvester equation are derived. Based on the derived norm upper bounds, new multiplicative perturbation bounds are provided both for subunitary polar factors and positive semi-definite polar factors. Some previous results are then improved.