Continuity and essential norm of operators defined by infinite tridiagonal matrices in weighted Orlicz and l∞ spaces

In this article, we provide a comprehensive study on the continuity and essential norm of an operator defined by an infinite tridiagonal matrix, specifically when it operates from a weighted Orlicz sequence space or a weighted l∞{l}^{\infty } space into another space of similar nature. Our findings include significant characterizations regarding the compactness of this operator across various contexts of weighted Orlicz and l∞{l}^{\infty } sequence spaces.