Abstract
We investigate a widely used application of compactness of bounded linear operators T: X(\BbbB) → Y, where X(\BbbB) is a Banach space of holomorphic functions on the open unit ball \BbbB ⊂ C N and Y is a Banach space. In particular, we show that compactness of the operator when X(\BbbB) is not reflexive, is not a sufficient condition for the property that every bounded sequence (fn) n∈ N in X(\BbbB) such that fn → 0 with respect to the compact open topology as n → ∞, implies that T(fn) → 0 with respect to the norm of Y as n → ∞.
| Original language | English |
|---|---|
| Pages (from-to) | 1153-1158 |
| Journal | Journal of Mathematical Inequalities |
| Volume | 18 |
| Issue number | 3 |
| DOIs | |
| Publication status | Published - Sept 2024 |
| MoE publication type | A1 Journal article-refereed |
Funding
Acknowledgement. The second author is grateful for the financial support from the Doctoral Network in Information Technologies and Mathematics at \u00C5bo Akademi University.