Spectral analysis of the quantum Cesàro operator over the sequence space l_p (1<p<infinity)

Nabadeep Kalita; Amar Jyoti Dutta

doi:10.5269/bspm.76020

Nabadeep Kalita Gauhati University
Amar Jyoti Dutta

Abstract

In this article, we study the spectrum, fine spectrum and boundedness property of $q-$Ces\`aro Matrices $C_1(q)$, which is a lower triangular matrix with $0<q<1$, over the class $\ell_p$~$(1<p<\infty)$, the $p^{th}$ summable sequence space. We determine the approximate point spectrum, defect spectrum, compression spectrum and Goldberg classification of the operator on the class of sequence. We construct the infinite system of linear equations of the given matrix operator to derive the results. Appropriate examples are provided along with graphical representations to support our study.

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