6 papers
The renorming-stable ball covering property and -spaces
Rui Liu, Jie Shen, Richard J. Smith
A Banach space has the ball-covering property (BCP) if its unit sphere can be covered by countably many balls that miss the origin. A Banach space has the renorming-stable ball-cov…
Duals of separable Banach Spaces as Calkin Algebras and Universal Ideal Quotients
Rui Liu, Jie Shen
For or and every separable Banach space , we use an oracle-relative two-sorted finite-extension construction, whose oracle records the local…
Inverse-Limit Detection Envelopes as Calkin Algebras
Rui Liu, Jie Shen
For a unital Banach algebra with and a decreasing sequence of proper closed two-sided ideals of finite codimension, we introduce the bounded detection envel…
-Properties, Uniformly Convexity and Uniform Ball Coverings Properties
Rui Liu, Jie Shen
In this paper, we prove a sufficient condition for the uniform ball-covering property of closed operator subspaces invariant under selected truncations. We use uniform convexity of…
Approximation properties and quantitative estimation for uniform ball-covering property of operator spaces
Qiyao Bao, Rui Liu, Jie Shen
In this paper, by dilation technique on Schauder frames, we extend Godefroy and Kalton's approximation theorem (1997), and obtain that a separable Banach space has the -uncondit…
The ball-covering property of non-commutative spaces of operators on Banach spaces
Qiyao Bao, Rui Liu, Jie Shen
A Banach space is said to have the ball-covering property (BCP) if its unit sphere can be covered by countably many closed or open balls off the origin. Let be a Banach space w…