Banach Spaces Which Embed into their Dual
V. Capraro, S. Rossi
TL;DR
This paper explores conditions under which Banach spaces can be embedded into their dual spaces, utilizing Birkhoff-James orthogonality to extend classical Riesz representation results.
Contribution
It introduces new conditions for embedding Banach spaces into their duals based on Birkhoff-James orthogonality, extending classical theorems.
Findings
New conditions for Banach space embeddings into duals
Extension of Riesz's representation theorem
Use of Birkhoff-James orthogonality in Banach space theory
Abstract
We use Birkhoff-James' orthogonality in Banach spaces to provide new conditions for the converse of the classical Riesz's representation theorem.
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Taxonomy
TopicsAdvanced Banach Space Theory · Functional Equations Stability Results · Holomorphic and Operator Theory