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Entropy numbers of diagonal operators on Orlicz sequence spaces
Author(s) -
Kaewtem Thanatkrit,
Netrusov Yuri
Publication year - 2021
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201900367
Subject(s) - mathematics , diagonal , sequence (biology) , entropy (arrow of time) , real number , pure mathematics , combinatorics , geometry , genetics , physics , quantum mechanics , biology
Let M 1 and M 2 be functions on [0,1] such thatM 1 ( t 1 / p ) andM 2 ( t 1 / p ) are Orlicz functions for some p ∈ ( 0 , 1 ] . Assume thatM 2 − 1( 1 / t ) / M 1 − 1( 1 / t )is non‐decreasing for t ≥ 1 . Let( α i ) i = 1 ∞ be a non‐increasing sequence of nonnegative real numbers. Under some conditions on( α i ) i = 1 ∞ , sharp two‐sided estimates for entropy numbers of diagonal operatorsT α : ℓM 1→ ℓM 2generated by( α i ) i = 1 ∞ , where ℓM 1and ℓM 2are 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].