Year: 2026
Type: preprint
Abstract: 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 the range space and near-contractive finite-rank projection approximations to obtain quantitative coverings with finite-rank centres whenever the truncated images are separable. A weak-star version gives the same covering parameters for quotients by arbitrary weak-star closed subspaces. In the completely bounded setting, the covering parameters are independent of the matrix level. In particular, the duals of all closed subspaces of $S_1(\ell_2)$ admit coverings with centre norm $2$ and radius $1+\varepsilon$, for $0<\varepsilon<1$, at every matrix level. Applications include operator-valued Schur multipliers and, for $1
Source: arXiv (Cornell University)
Language: English
Topic: Advanced Banach Space Theory
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: G7991042
OpenAlex ID: W7168413005