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Essential norms of pointwise multipliers acting between K\"othe spaces: Non-algebraic case

Tomasz KiwerskiJakub Tomaszewski
Dec 2022
摘要
Motivated by some recent results, but also referring to classics, we computethe essential norm and the weak essential norm of the multiplication operatorsacting between two different K\"othe spaces both defined over the same completeand $\sigma$-finite measure space. A by-product of the technology we havedeveloped here are some applications to the abstract Ces\'aro spaces, theirduals, the abstract Tandori spaces, and Banach spaces of analytic functions onthe unit disc (in particular, abstract Hardy spaces). We will close our workwith some specific examples illustrating the previously obtained resultsincluding Orlicz and Musielak--Orlicz sequence spaces (in particular, Nakanosequence spaces) as well as Lorentz and Marcinkiewicz sequence spaces.
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