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Vector valued paranormed bounded and null sequence spaces associated with multiplier sequences. (English) Zbl 1043.46013

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.

MSC:

46A45 Sequence spaces (including Köthe sequence spaces)
40A05 Convergence and divergence of series and sequences
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