On Certain Sequence Space
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Keywords:
Sequence space, BK space, Schauder basis, K\Abstract
In this paper, we introduce a new sequence space $\ell_s^p, \, p \geq 1,$ which turns out to be an infinite dimensional separable Banach space in which H\"{o}lder inequality does not hold. It is shown that it is a proper subspace of $\ell^p$ to which $\ell^p $ is topologically equivalent. Apart from studying various algebraic and topological properties of $\ell_s^p$, its K\"{o}the- Toeplitz duals have also been computed.
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This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.