On weakly sequentially complete Banach spaces
E. M. Bednarczuk, K. Le\'sniewski
TL;DR
This paper establishes sufficient conditions for a Banach space to be weakly sequentially complete, based on the existence of directional derivatives for cone convex mappings with values in that space.
Contribution
It introduces new criteria linking weak sequential completeness to directional derivatives of cone convex mappings in Banach spaces.
Findings
Conditions for weak sequential completeness established
Directional derivatives play a key role in the criteria
Provides a new perspective on Banach space properties
Abstract
We provide sufficient conditions for a Banach space Y to be weakly sequentially complete. These conditions are expressed in terms of the existence of directional derivatives for cone convex mappings with values in Y .
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Taxonomy
TopicsAdvanced Banach Space Theory · Optimization and Variational Analysis · Nonlinear Differential Equations Analysis