Some Geometric Properties of the Cesàro Function Spaces

Some geometric properties of the Cesàro function spaces

,

1\leqslant p<\infty 1 ⩽ p < ∞

, induced by an arbitrary positive weight function

w w

on an interval

(0,l) ( 0 , l )

where

0 < l \leqslant\infty 0 < l ⩽ ∞

are studied in this paper. It is shown that all non-empty relatively weakly open sets in the unit ball of

C_{p,w} C p , w

have diameter

2 2

. Also

C_{p,w} C p , w

,

1<p<\infty 1 < p < ∞

is strictly convex but no point of its unit ball is strongly extreme. Moreover, some connections between uniformly non-square points and various geometric properties in general Banach spaces are presented.