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BANACH-SAKS PROPERTIES OF MUSIELAK-ORLICZ AND NAKANO SEQUENCE SPACES
- Authors
- Kaminska, Anna; Lee, Han Ju
- Issue Date
- Feb-2014
- Publisher
- AMER MATHEMATICAL SOC
- Keywords
- Banach-Saks properties; Schur property; Musielak-Orlicz space; Nakano space; variable exponent space; weighted Orlicz space
- Citation
- PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, v.142, no.2, pp 547 - 558
- Pages
- 12
- Indexed
- SCI
SCIE
SCOPUS
- Journal Title
- PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
- Volume
- 142
- Number
- 2
- Start Page
- 547
- End Page
- 558
- ISSN
- 0002-9939
1088-6826
- Abstract
- In this paper Banach-Saks properties of Musielak-Orlicz sequence space l(phi) F are studied. It is shown that l(phi) F has the weak Banach-Saks property if and only if it is separable. Moreover it is proved that in l(phi) F both Banach-Saks type p-properties, (BSp) and (S-p), are equivalent and that the Schur property and (BS infinity) also coincide in these spaces. As applications, we give characterizations of the weak Banach-Saks property and the (BSp) property in the Nakano sequence space l((pn)) and weighted Orlicz sequence space l(phi)(w), in terms of the sequence (p(n)), and the Orlicz function phi and the weight sequence w, respectively.
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Related Researcher
- Lee, Han Ju
- College of Education (Department of Mathematics Education)