论文标题
季源Banach代数中的弗雷霍尔姆理论
Fredholm theory in quaternionic Banach algebras
论文作者
论文摘要
Muraleetharan和Thirulogasanthan（J.Math。Phys。59，No. 10，103506，27p。（2018））介绍了有界的Quaternionic线性运算符的Calkin Spectrum的概念。该频谱的研究是使用弗雷德霍尔姆操作员理论建立的。在此激励的情况下，我们研究了Fredholm元素的一般框架，相对于Quaternionic Banach代数同态。首先，我们通过两个元素的Fredholm s-spectrum研究了Quaternion Banach代数中两个元素的弗雷姆S谱。接下来，我们证明了该频谱上的扰动结果。我们还研究边界s光谱。作为应用，我们研究了有限的右Quaternion线性算子的Fredholm和Weyl s-Spectra。
Muraleetharan and Thirulogasanthan in (J. Math. phys. 59, No. 10, 103506, 27p. (2018)) introduced the concept of Calkin Sspectrum of a bounded quaternionic linear operators. The study of this spectrum is establisched using the Fredholm operators theory. Motivated by this, we study the general framework of the Fredholm element with respect to a quaternionic Banach algebra homomorphism. First, we investigate the Fredholm S-spectrum of the sum of two elements in quaternionic Banach algebra by means of the Fredholm S-spectrum of the two elements. Next, we prove a perturbation result on this spectrum. We also study the boundary S-spectrum. As application, we investigate the Fredholm and Weyl S-spectra of bounded right quaternionic linear operators.
