Uniform property (K) and its related properties
Hong‐Kun Xu, Giuseppe Marino · Bulletin of the Australian Mathematical Society · 1998
A Banach space X is said to have uniform property (K) if there exists a constant (k ∈ [0,1) such that whenever xn ⇀ 0, ∥xn∥ → 1, and we have lim sup ∥ym∥ ≤ k. This property is the uniform version of property (K) recently introduced by B. Sims (Bull. Austral. Math. Soc. 50(1994), 523–528). Sufficient conditions for uniform property (K) are given. Some examples are presented to separate various Banach space properties. Applications to nonlinear operators are also included.