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Zeitschrift für Analysis und ihre Anwendungen

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Volume 13, Issue 2, 1994, pp. 181–189
DOI: 10.4171/ZAA/517

Published online: 1994-06-30

On the Nakano Individual Convergence

R. Zaharopol[1]

(1) Binghamton University, USA

We have recently defined the notion of individual convergence for a sequence of positive elements of an Archimedean Riesz space $E$. In the note we complete the definition (i.e., we define the individual convergence for sequences of not necessarily positive elements of $E$), and we prove that our notion of individual convergence is a natural extension of the individual convergence as defined by Nakano: we will prove that if a sequence of elements of $E$ has an individual limit in the Nakano sense, then it converges individually with respect to our definition.

Keywords: Archimedean Riesz spaces, Dedekind completion, projection bands, Nakano individual convergence

Zaharopol R.: On the Nakano Individual Convergence. Z. Anal. Anwend. 13 (1994), 181-189. doi: 10.4171/ZAA/517