On Certain Sequence Space - Sandeep Gupta (International Journal of Mathematics And its Applications, 2018)
In this paper, we introduce a new sequence space $\ell_s^p, \, p ≥ 1,$ which turns out to be an infinite dimensional separable Banach space in which Hölder 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 Köthe- Toeplitz duals have also been computed.