On the linearity of some sets of sequences defined by $L_{p}$-functions and $L_{1}$-functions determining $\ell_{1}$
Nakamura, Gen ; Hashimoto, Kazuo
Proc. Japan Acad. Ser. A Math. Sci., Tome 87 (2011) no. 1, p. 77-82 / Harvested from Project Euclid
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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 $f\in BV(\mathbf{R})$.
Publié le : 2011-05-15
Classification:  Sequence space,  linearity,  essential bounded variation,  Sobolev space,  46A45,  46E35,  65B20 
@article{1303825551,
     author = {Nakamura, Gen and Hashimoto, Kazuo},
     title = {On the linearity of some sets of sequences defined by $L\_{p}$-functions and $L\_{1}$-functions determining $\ell\_{1}$},
     journal = {Proc. Japan Acad. Ser. A Math. Sci.},
     volume = {87},
     number = {1},
     year = {2011},
     pages = { 77-82},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1303825551}
}

Nakamura, Gen; Hashimoto, Kazuo. On the linearity of some sets of sequences defined by $L_{p}$-functions and $L_{1}$-functions determining $\ell_{1}$. Proc. Japan Acad. Ser. A Math. Sci., Tome 87 (2011) no. 1, pp.  77-82. http://gdmltest.u-ga.fr/item/1303825551/