Abstract
In this article, we define the generalized cesaro sequence spaces ces(p)(q) and consider it equipped with the Luxemburg norm. We show that the spaces ces(p)(q) has the H-property and Uniform Opial property. The results of this article, we improve and extend some results of Petrot and Suantai.
Highlights
Let (X, || · ||) be a real Banach space and let B(X) (resp., S(X)) be a closed unit ball of X
A point x Î S(X) is an H-point of B(X) if for any sequence in X such that ||xn|| ® 1 as n ® ∞, the week convergence of to x implies that ||xn - x|| ® 0 as n ® ∞
Let l0 be the space of all real sequences
Summary
Let (X, || · ||) be a real Banach space and let B(X) (resp., S(X)) be a closed unit ball (resp., the unit sphere) of X. A Banach space X is said to have the Opial property (see [1]), if every weakly null sequence (xn) in X satisfies lim n→∞ Opial proved in [1] that the sequence space lp(1 < p < ∞) have this property but Lp[0, π](p ≠ 2, 1 < p < ∞) do not have it.
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