Tripathy, Binod Chandra; Sen, Mausumi Vector valued paranormed bounded and null sequence spaces associated with multiplier sequences. (English) Zbl 1043.46013 Soochow J. Math. 29, No. 3, 313-326 (2003). Summary: In this article, we introduce the multiplier vector valued sequence spaces \(\ell_\infty \{E_k,\Lambda,p\}\) and \(c_0\{E_k, \Lambda,p\}\), where \(\Lambda=(\gamma_k)\) is an associated multiplier sequence of non-zero complex numbers and the terms of the sequence are chosen from the seminormed spaces \(E_k\), \(k\in \mathbb{N}\). This generalizes the scalar sequence spaces \(\ell_\infty\{p\}\) and \(c_0\{p\}\). We study some properties of these spaces like solidity, completeness and prove some inclusion results. We characterize the multiplier problem and obtain their duals. Cited in 6 Documents MSC: 46A45 Sequence spaces (including Köthe sequence spaces) 40A05 Convergence and divergence of series and sequences Keywords:multiplier sequence spaces; solidity; completeness; inclusion results; multiplier problem PDFBibTeX XMLCite \textit{B. C. Tripathy} and \textit{M. Sen}, Soochow J. Math. 29, No. 3, 313--326 (2003; Zbl 1043.46013)