2013
DOI: 10.1080/01630563.2013.775591
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One-Complemented Subspaces in Musielak-Orlicz Sequence Spaces with a General Smoothness Condition

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Cited by 1 publication
(7 citation statements)
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“…Actually, in this article we will compare contractive and optimal sets defined in a more general way using the modular, since our study is devoted to a wide class of Musielak-Orlicz sequence spaces. This will be done precisely using the main result of [6] and some arguments of Kamińska and Lewicki from [12]. Our results complete in some sense the results from [12] providing a characterization of strongly contractive sets in the sense of the modular ρ Φ in a Musielak-Orlicz space (n) Φ when Φ satisfies condition (M ).…”
Section: Anna Denkowskamentioning
confidence: 61%
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“…Actually, in this article we will compare contractive and optimal sets defined in a more general way using the modular, since our study is devoted to a wide class of Musielak-Orlicz sequence spaces. This will be done precisely using the main result of [6] and some arguments of Kamińska and Lewicki from [12]. Our results complete in some sense the results from [12] providing a characterization of strongly contractive sets in the sense of the modular ρ Φ in a Musielak-Orlicz space (n) Φ when Φ satisfies condition (M ).…”
Section: Anna Denkowskamentioning
confidence: 61%
“…Condition (S), though not really restrictive, excludes such regular functions as t p for p ∈ [1, 2) (thus the Jamison-Kamińska-Lewicki Theorem does not not work for p ). In [6] we generalized Theorem 2.7 from [11] to the case of Musielak-Orlicz functions satisfying a smoothness condition (S ) (Definition 3.4) and obtained an analogous characterization with a mixed condition (M ).…”
Section: Anna Denkowskamentioning
confidence: 99%
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