MATEMATIČKI VESNIK
МАТЕМАТИЧКИ ВЕСНИК



MATEMATIČKI VESNIK
Application of the infinite matrix theory to the solvability of certain sequence spaces equations with operators
Bruno de Malafosse

Abstract

In this paper we deal with special {\it sequence spaces equations (SSE) with operators}, which are determined by an identity whose each term is a {\it sum or a sum of products of sets of the form $\chi_{a}(T)$ and $\chi_{f(x)}(T)$} where $f$ maps $U^{+}$ to itself, and $\chi$ is any of the symbols $s$, $s^{0}$, or $s^{(c)}$. We solve the equation $\chi_{x}(\Delta )=\chi_{b}$ where $\chi$ is any of the symbols $s$, $s^{0}$, or $s^{(c)}$ and determine the solutions of (SSE) with operators of the form $(\chi_{a}\ast\chi_{x}+\chi_{b})(\Delta)=\chi_{\eta}$ and $[\chi_{a}\ast(\chi_{x})^{2}+\chi_{b}\ast\chi_{x}](\Delta)=\chi_{\eta}$ and $\chi_{a}+\chi_{x}(\Delta)=\chi_{x}$ where $\chi$ is any of the symbols $s$, or $s^{0}$.

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Keywords: Sequence space; operator of the first difference; BK space; infinite matrix; sequence spaces equations (SSE); (SSE) with operators.

MSC: 40C05, 46A15

Pages:  39--52     

Volume  64 ,  Issue  1 ,  2012