METRICS ON THE SEQUENCE SPACE Λp (f)
スポンサーリンク
概要
- 論文の詳細を見る
For 1 ≤ p, r <+∞, f (≠ 0) ∈ Lp (R, dx), and g (≠ 0) ∈ Lr (R, dx), the sequence space Λp (f) with metric dfp(a,b) was introduced in a previous paper and we discussed the inclusion relations between lp and Λp (f), and the linearity of Λp (f).The purpose of this paper is to discuss the topological structures of (Λp (f), dfp).First we show that the space (Λp (f), dfp) is a complete separable metric group. Next we show that if Λp (f) is a linear space, then (Λp (f), dfp) is a topological linear space. On the other hand, we give a necessary and sufficient condition for the inclusion Λp (f) ⊂ Λr (g). Furthermore, we show that the inclusions among the sequence spaces Λp (f), Λr (g) and lr are continuous. The fact that Λp (f) ⊂ Λr (g) as sets implies the continuity of the inclusion (Λp (f), dfp) → (Λr (g), dgr) is emphasized.
著者
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Honda Aoi
Department Of Control Engineering And Science Faculty Of Computer Science And Systems Engineering Ky
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Okazaki Yoshiaki
Department Of Systems Design And Informatics Kyushu Institute Of Technology
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Okazaki Yoshiaki
Department Of Artificial Intelligence Kyushu Inst. Of Technology
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Sato Hiroshi
Faculty of Education and Human Science, University of Yamanashi
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HONDA Aoi
Department of Systems Design and Informatics Kyushu Institute of Technology
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