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May 2011 On the linearity of some sets of sequences defined by $L_{p}$-functions and $L_{1}$-functions determining $\ell_{1}$
Gen Nakamura, Kazuo Hashimoto
Proc. Japan Acad. Ser. A Math. Sci. 87(5): 77-82 (May 2011). DOI: 10.3792/pjaa.87.77

Abstract

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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Gen Nakamura. Kazuo Hashimoto. "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. 87 (5) 77 - 82, May 2011. https://doi.org/10.3792/pjaa.87.77

Information

Published: May 2011
First available in Project Euclid: 26 April 2011

zbMATH: 1252.46004
MathSciNet: MR2803895
Digital Object Identifier: 10.3792/pjaa.87.77

Subjects:
Primary: 46A45 , 46E35
Secondary: 65B20

Keywords: essential bounded variation , linearity , sequence space , Sobolev space

Rights: Copyright © 2011 The Japan Academy

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Vol.87 • No. 5 • May 2011
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