Entropy numbers of diagonal operators on Orlicz sequence spaces

Thanatkrit Kaewtem and Yuri Netrusov

Mathematische Nachrichten, 2021, vol. 294, issue 7, 1350-1373

Abstract: Let M1 and M2 be functions on [0,1] such that M1(t1/p) and M2(t1/p) are Orlicz functions for some p∈(0,1]. Assume that M2−1(1/t)/M1−1(1/t) is non‐decreasing for t≥1. Let (αi)i=1∞ be a non‐increasing sequence of nonnegative real numbers. Under some conditions on (αi)i=1∞, sharp two‐sided estimates for entropy numbers of diagonal operators Tα:ℓM1→ℓM2 generated by (αi)i=1∞, where ℓM1 and ℓM2 are Orlicz sequence spaces, are proved. The results generalise some works of Edmunds and Netrusov in [8] and hence a result of Cobos, Kühn and Schonbek in [6].

Date: 2021
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