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On the Domain of Riesz Mean in the Space ℒ
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Journal Article
On the Domain of Riesz Mean in the Space ℒ
2017
Overview
Let 0 < 𝑠 < ∞. In this study, we introduce the double sequence space 𝑅𝑞𝑡(𝓛𝑠) as the domain of four dimensional Riesz mean 𝑅𝑞𝑡in the space 𝓛𝑠of absolutely 𝑠-summable double sequences. Furthermore, we show that 𝑅𝑞𝑡(𝓛𝑠) is a Banach space and a barrelled space for 1 ≤ 𝑠 < ∞ and is not a barrelled space for 0 < 𝑠 < 1. We determine the 𝛼- and 𝛽(𝑣)-duals of the space 𝓛𝑠for 0 < 𝑠 ≤ 1 and 𝛽(𝑏𝑝)-dual of the space 𝑅𝑞𝑡(𝓛𝑠) for 1 < 𝑠 < ∞, where 𝑣∈{𝑝,𝑏𝑝,𝑟}. Finally, we characterize the classes (𝓛𝑠: 𝛭𝑢), (𝓛𝑠: 𝐶𝑏𝑝), (𝑅𝑞𝑡(𝓛𝑠) : 𝛭𝑢) and (𝑅𝑞𝑡(𝓛𝑠) : 𝐶𝑏𝑝) of four dimensional matrices in the cases both 0 < 𝑠 < 1 and 1 ≤ 𝑠 < ∞ together with corollaries some of them give the necessary and sufficient conditions on a four dimensional matrix in order to transform a Riesz double sequence space into another Riesz double sequence space.
Publisher
Faculty of Sciences and Mathematics, University of Niš
Subject
