Solvability of the Sequence Spaces Equations With Operators Ca+Cx = (Cb)B(r,s) And Ca+Cx = (Cb)G(α,α)

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Authors

  • Bruno De Malafosse
     Department of Mathematics, University of Le Havre, 76600 Le Havre ,FR

DOI:

https://doi.org/10.18311/jims/2022/29308

Keywords:

BK space, matrix transformations, multiplier of sequence spaces, sequence spaces equations, sequence spaces equations with operator

Abstract

Given any sequence a = (an)n?1 of positive real numbers and any set E of complex sequences, we write Ea for the set of all sequences y = (yn)n?1 such that y/a = (yn/an)n?1 ? E; in particular, ca, (or s(c) a ) denotes the set of all sequences y such that y/a converges. In this paper, we solve sequence spaces equations of the form (Ex)B(r,s) = Ea, where E 2 {c0, c, `1}. Then we apply these results to the solvability of each of the (SSE) with operators ca + cx = (cb)B(r,s) and ca + cx = (cb)G(,), where B (r, s) is a double band matrix, and G(, ) is the factorable matrix with positive sequences and , that is, the triangle whose the nonzero entries are defined by [G(, )]nk = nk.

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Published

2022-01-27

How to Cite

Malafosse, B. D. (2022). Solvability of the Sequence Spaces Equations With Operators C<sub>a</sub>+C<sub>x</sub> = (C<sub>b</sub>)<sub>B</sub><sub>(r,s)</sub> And C<sub>a</sub>+C<sub>x</sub> = (C<sub>b</sub>)<sub>G</sub><sub>(α,α)</sub>. The Journal of the Indian Mathematical Society, 89(1-2), 84–99. https://doi.org/10.18311/jims/2022/29308

Issue

Volume 89, Issue 1-2, January-June 2022

Section

Articles

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Copyright (c) 2022 Bruno De Malafosse

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This work is licensed under a Creative Commons Attribution 4.0 International License.

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Europe PMC
Received 2022-01-11
Accepted 2023-01-30
Published 2022-01-27

 

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