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 Tu,v,w{T}_{u,v,w} acting on the weighted sequence space lβ2{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 Mu{M}_{u} acting on lβ2{l}_{\beta }^{2} spaces was calculated.

Keywords

• compact operators
• essential norm
• multiplication operator
• primary: 47b60
• 46b45
• secondary: 46e30
• 46b42