On The Spectrum Of Norlund Type Matrix Operator 𝐴 = (𝑎𝑛𝑘) On The Sequence Spaces ℓ1 And 𝑏𝑣

Abstract

In this article, we defined a Nörlund type matrix 𝐴 = (𝑎𝑛𝑘) by 𝑎𝑛𝑘 = { 1 , 𝑘 = 𝑛 = 0 1 2 , 𝑛 − 1 ≤ 𝑘 ≤ 𝑛 0 , 𝑜𝑡ℎ𝑒𝑟𝑣𝑖𝑠𝑒 . Then we showed that the Nörlund type matrix 𝐴 = (𝑎𝑛𝑘) is a linear and bounded operator on the sequence spaces ℓ1 and 𝑏𝑣. Finally, we calculated the fine spectrum and its subdivisions of the operator 𝐴 = (𝑎𝑛𝑘) on the sequence spaces ℓ1 and 𝑏𝑣.

Keywords

• sequence space
• bounded variation
• nörlund type matrix
• bounded operators
• spectrum of an operator