2016/06/20 by Riddhick Birbonshi, R. Birbonshi, Birbonshi, R. +2
Computer Science · Mathematics · #47A10 #47B37 #Approximation Theory and Sequence Spaces #FOS: Mathematics #Holomorphic and Operator Theory #Matrix Theory and Algorithms #Spectral Theory (math.SP) #math.SP #msc:47A10 #msc:47B37
paper · pdf · doi:10.48550/arxiv.1606.05993
There are some error in the proof
openalex publication_date 2016/06/20 · arxiv created 2017/05/27 · arxiv updated 2017/05/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 c0, lp and bvp. 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 (≥4) band lower triangular matrices over the sequence spaces c0, lp and bvp. 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|≤ 1 under a polynomial of degree n≥ 1 which plays the key role in our study. Similar studies has also been done for the sequence spaces c, l1, bv and l_∞. Upper triangular matrices has also been investigated for some sequence spaces.