| On a Class of Vector-Valued Sequences Associated with Multiplier Sequences |
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| 作者姓名： | BinodChandraTripathy SabitaMahanta |
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| 作者单位： | Binod Chandra Tripathy~1 Sabita Mahanta~2 Mathematical Sciences Division,Institute of Advanced Study in Science and Technology,Khanapara,Guwahati-781022,India (E-mail:tripathybc@yahoo.coln),(E-mail:sabitamahanta@yahoo.co.in) |
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| 摘 要： | In this article we introduce the vector valued sequence space m(E_k,φ,∧),associated with themultiplier sequence ∧=(λ_k) of non-zero complex numbers,and the terms of the sequence are chosen from theseminormed spaces E_k,seminormed by f_k for all k∈N.This generalizes the sequence space m(φ) introducedand studied by Sargent.We study some of its properties like solidity,completeness,and obtain some inclusionresults.We also characterize the multiplier problem and obtain the corresponding spaces dual to m(E_k,φ,∧).We prove some general results too.
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| 关 键 词： | 乘法序列空间 固体空间 完全性 双重性 均衡空间 数学分析 |
| 收稿时间： | 12 January 2004 |
On a Class of Vector-Valued Sequences Associated with Multiplier Sequences |
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| BinodChandraTripathy SabitaMahanta.On a Class of Vector-Valued Sequences Associated with Multiplier Sequences[J].Acta Mathematicae Applicatae Sinica,2004,20(3):487-494. |
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| Authors: | Email author" target="_blank">Binod?Chandra?TripathyEmail author Sabita?Mahanta |
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| Institution: | (1) Mathematical Sciences Division, Institute of Advanced Study in Science and Technology, Khanapara, Guwahati-781022, India |
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| Abstract: | Abstract
In this article we introduce the vector valued sequence space m(E
k
, φ, Λ), associated with the multiplier sequence Λ = (λ
k
) of non-zero complex numbers, and the terms of the sequence are chosen from the seminormed spaces E
k
, seminormed by f
k
for all k ∈ N. This generalizes the sequence space m(φ) introduced and studied by Sargent10]. We study some of its properties like solidity, completeness, and obtain some inclusion results. We also characterize the
multiplier problem and obtain the corresponding spaces dual to m(E
k
, φ, Λ). We prove some general results too. |
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| Keywords: | Multiplier sequence space solid space completeness dual symmetric space |
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