On Certain Sequence Space

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.