Banach-Saks index in spaces with symmetric basis

The Banach-Saks index of some sequence spaces

“…The constant in the right inequality cannot be improved since for every 0 < < 1 there exist 1 < p < q < ∞ such that 1 p + 1 q = 2 − (with 1 p + 1 p = 1 and 1 q + 1 q = 1), while γ(l p,q ) = min(p, q) = p and γ(l * p,q ) = γ(l p ,q ) = min(p , q ) = q [11]. Here l p,q is the Lorentz sequence space equipped with the norm…”