On the linearity of some sets of sequences defined by $L_{p}$-functions and $L_{1}$-functions determining $\ell_{1}

In this paper, we discuss the linearity of a sequence space \Lambda_{p}(f), and the conditions such that \ell_{1} = \Lambda_{1}(f) holds are characterized in term of the essential bounded variation of f\in L_{1}(\mathbf{R}), i.e. \ell_{1} = \Lambda_{1}(f) if and only if f\in BV(\mathbf{R}).

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Bibliographic Details
Published inProceedings of the Japan Academy. Series A. Mathematical sciences Vol. 87; no. 5; pp. 77 - 82
Main Authors Nakamura, Gen, Hashimoto, Kazuo
Format Journal Article
LanguageEnglish
Published The Japan Academy 01.05.2011
Subjects
46A45
46E35
65B20
essential bounded variation
linearity
Sequence space
Sobolev space
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Summary:In this paper, we discuss the linearity of a sequence space \Lambda_{p}(f), and the conditions such that \ell_{1} = \Lambda_{1}(f) holds are characterized in term of the essential bounded variation of f\in L_{1}(\mathbf{R}), i.e. \ell_{1} = \Lambda_{1}(f) if and only if f\in BV(\mathbf{R}).
ISSN:0386-2194
DOI:10.3792/pjaa.87.77