On the compactness and the essential norm of operators defined by infinite tridiagonal matrices

Abstract

In this article, all sequences u {\boldsymbol{u}} , v {\boldsymbol{v}} , and w {\boldsymbol{w}} that define continuous and compact tridiagonal operators T u , v , w {T}_{u,v,w} acting on the weighted sequence space l β 2 {l}_{\beta }^{2} were characterized. Additionally, the essential norm of this operator, and as an important consequence of our results, the essential norm of multiplication operator M u {M}_{u} acting on l β 2 {l}_{\beta }^{2} spaces was calculated.