Ball covering property from commutative function spaces to non-commutative spaces of operators
Abstract
A Banach space is said to have the ball-covering property (abbreviated BCP) if its unit sphere can be covered by countably many closed, or equivalently, open balls off the origin. Let K be a locally compact Hausdorff space and X be a Banach space. In this paper, we give a topological characterization of BCP, that is, the continuous function space C0(K) has the (uniform) BCP if and only if K has a countable π-basis. Moreover, we give the stability theorem: the vector-valued continuous function space C0(K,X) has the (strong or uniform) BCP if and only if K has a countable π-basis and X has the (strong or uniform) BCP. We also explore more examples for BCP on non-commutative spaces of operators B(X,Y). In particular, these results imply that B(c0), B(ℓ1) and every subspace containing finite rank operators in B(ℓp) for 1
Publication Title
Journal of Functional Analysis
Recommended Citation
Liu, M., Liu, R., Lu, J., & Zheng, B. (2022). Ball covering property from commutative function spaces to non-commutative spaces of operators. Journal of Functional Analysis, 283 (1) https://doi.org/10.1016/j.jfa.2022.109502
