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2013 Matrix transformations and sequence spaces equations
Vladimir Rakocevic , Bruno de Malafosse
Banach J. Math. Anal. 7(2): 1-14 (2013). DOI: 10.15352/bjma/1363784219

## Abstract

In this paper we study sequence spaces equations (SSE) with operators, which are determined by an identity whose each term is a sum or a sum of products of sets of the form $\chi _{a}\left( T\right)$ and $\chi _{f\left( x\right) }\left( T\right)$ where $f$ maps $U^{+}$ to itself, $\chi$ is either of the symbols $s$, $s^{0}$, or $s^{\left( c\right) }$. Then we solve five (SSE) of the form $\chi _{a}+\chi _{x}^{\prime }=\chi _{b}^{\prime }$, where $\chi$, $\chi ^{\prime }$ are either $s^{{{}0}}$, $s^{\left( c\right) }$, or $s$. We apply the previous results to the solvability of the systems $s_{a}^{0}+s_{x}\left( \Delta \right) =s_{b}$, $s_{x}\supset s_{b}$ and $s_{a}+s_{x}^{\left( c\right) }\left( \Delta \right) =s_{b}^{\left( c\right) }$, $s_{x}^{\left( c\right) }\supset s_{b}^{\left( c\right) }$. Finally we solve the (SSE) with operators defined by $\chi _{a}\left( C\left( \lambda \right) D_{\tau }\right) +s_{x}^{\left( c\right) }\left( C\left( \mu \right) D_{\tau }\right) =s_{b}^{\left( c\right) }$ where $\chi$ is either $s^{0}$, or $s$.

## Citation

Vladimir Rakocevic . Bruno de Malafosse . "Matrix transformations and sequence spaces equations." Banach J. Math. Anal. 7 (2) 1 - 14, 2013. https://doi.org/10.15352/bjma/1363784219

## Information

Published: 2013
First available in Project Euclid: 20 March 2013

zbMATH: 1270.40008
MathSciNet: MR3039935
Digital Object Identifier: 10.15352/bjma/1363784219

Subjects:
Primary: 40H05
Secondary: 46A45

Keywords: BK space , matrix transformations , multiplier of sets of sequences , sequence spaces equations with operator , sequence spaces inclusion equations , sequence spaces inclusion equations

Rights: Copyright © 2013 Tusi Mathematical Research Group

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Vol.7 • No. 2 • 2013