关于$n$ -带三角形矩阵精细谱的一些研究
On some study of the Fine Spectra of $n$-th band triangular matrices
摘要：
已经观察到，对于第二和第三带下三角形矩阵$B(r,s)$和$B(r,s,t)$，只有谱的边界给出连续谱，而整个内部区域的其余部分给出序列空间$c_0$、$l_p$和$bv_p$上的剩余谱。本文主要研究序列空间$c_0$、$l_p$和$bv_p$上的$n (\ge4)$带下三角形矩阵的类似行为发生的可能性.结果表明，不仅边界部分，但从频谱的内部区域的有限集被包括在连续谱，而相同的集合被排除在剩余谱。在这方面，我们已经证明了一个有趣的结果，关于图像的封闭单位盘$|z|\le 1$下的多项式的次数$n\ge 1$，这在我们的研究中起着关键作用。对序列空间$c$、$l_1$、$bv$和$l_\infty$也进行了类似的研究。在某些序列空间上也研究了上三角形矩阵。
英文摘要：
It has been observed that for the 2nd and 3rd band lower triangular matrices $B(r,s)$ and $B(r,s,t)$, only the boundary of the spectrum gives the continuous spectrum while the rest of the entire interior region gives the residual spectrum over the sequence spaces $c_0$, $l_p$ and $bv_p$. The main focus of our present study is to investigate the possibilities of the occurrence of the similar kinds of behavior for the cases of $n (\ge4)$ band lower triangular matrices over the sequence spaces $c_0$, $l_p$ and $bv_p$. The outcomes depicts that not only the boundary part but a finite set from the interior region of the spectrum is included in the continuous spectrum while the same set is excluded from the residual spectrum. In this context, we have proved an interesting result regarding the image of the closed unit disk $|z|\le 1$ under a polynomial of degree $n\ge 1$ which plays the key role in our study. Similar studies has also been done for the sequence spaces $c$, $l_1$, $bv$ and $l_\infty$. Upper triangular matrices has also been investigated for some sequence spaces.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
