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

In this article, all sequences u, v, and w that define continuous and compact tridiagonal operators Tu,v,w acting on the weighted sequence space l β 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 acting on l β 2 spaces was calculated. © 2023 the author(s), published by De Gruyter.