Another look at Cesàro sequence spaces

Abstract

We consider the Cesàro sequence space ces p as a closed subspace of the infinite p -sum of finite dimensional spaces. We easily obtain many known results, for example, ces p has property (β) of Rolewicz, uniform Opial property, and weak uniform normal structure.We also consider some generalized Cesàro sequence spaces. Finally, we compute the von Neumann-Jordan and James constants of the two-dimensional Cesàro sequence space ces(2) p when 1 < p 2.

Multiplier and averaging operators in the Banach spaces $$\mathbf{ces(p), \, 1< p < \infty }$$ ces ( p ) , 1 < p < ∞

“…with each E n , n ∈ N, a nite dimensional space, [21,Theorem 1], it follows that ℓ p is isomorphic to a closed subspace of…”

Certain geometric structures of $\Lambda$-sequence spaces

“…2 ) 2 ≤ C NJ (Λ (see [19], [27]). The following theorem is a counter part of a theorem presented in ( [27], Theorem 15, p.536) for the sequence space Λ (2) p . We repeat here for the sake of completeness.…”

Some topological properties of double Ces aro-Orlicz sequence spaces

“…In the case, when M(u) = |u| p , 1 ≤ p < ∞, we get the Cesaro sequence spaces Ces p . The topological and geometric properties of Cesàro-Orlicz sequence spaces and their generalizations have been studied in [2], [3], [5], [7], [13], [14].…”