Collective compactness, equicompactness and the degree of nondensifiability
Submitted: 2025-03-29
|Accepted: 2025-11-10
|Published: 2026-02-24
Copyright (c) 2025 Gonzalo García
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
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Keywords:
linear operators, compact operators, collectively compact operators, equicompact operators, degree of nondensifiability, $\alpha$-dense curves
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Abstract:
The degree of nondensifiability (DND) quantifies, in a specific sense, the distance between a bounded subset of a metric space and the Peano Continua it contains. In this paper, we use the DND to establish a quantitative version of the concepts of collective compactness and equicompactness for families of bounded linear operators between Banach spaces. Specifically, we prove inequalities that relate the DND to these notions and through some examples, we demonstrate that these inequalities are the best possible
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