Analysis reveals the continuity and essential norm of operators defined by infinite tridiagonal matrices, suggesting implications for compactness in weighted Orlicz 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 <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msup> <m:mrow> <m:mi>l</m:mi> </m:mrow> <m:mrow> <m:mi>∞</m:mi> </m:mrow> </m:msup> </m:math> {l}∞ 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 <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msup> <m:mrow> <m:mi>l</m:mi> </m:mrow> <m:mrow> <m:mi>∞</m:mi> </m:mrow> </m:msup> </m:math> {l}∞ sequence spaces.
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Ramos-Fernández et al. (2025) studied this question.
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