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On a Class of Vector-Valued Sequences Associated with Multiplier Sequences

On a Class of Vector-Valued Sequences Associated with Multiplier Sequences 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 Sargent[10]. 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

On a Class of Vector-Valued Sequences Associated with Multiplier Sequences

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References (10)

Publisher
Springer Journals
Copyright
Copyright © 2004 by Springer-Verlag Berlin Heidelberg
Subject
Mathematics; Applications of Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics
ISSN
0168-9673
eISSN
1618-3932
DOI
10.1007/s10255-004-0186-7
Publisher site
See Article on Publisher Site

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 Sargent[10]. 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.

Journal

Acta Mathematicae Applicatae SinicaSpringer Journals

Published: Jan 1, 2004

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