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EnglishWe prove that if a Banach space admits a biorthogonal system whose dual part is norming, then the set of norm-attaining functionals is lineable. As a consequence, if a Banach space admits a biorthogonal system whose dual part is bounded and its weak-star closed absolutely convex hull is a generator system, then the Banach space can be equivalently renormed so that the set of norm-attaining functionals is lineable. Finally, we prove that every infinite dimensional separable Banach space whose dual unit ball is weak-star separable has a linearly independent, countable, weak-star dense subset in its dual unit ball. As a consequence, we show the existence of linearly independent norming sets which are not the dual part of a biorthogonal system.
| Titolo: | Renormings concerning the lineability of the norm-attaining functionals | |
| Autori interni: | ||
| Data di pubblicazione: | 2017 | |
| Rivista: | ||
| Handle: | http://hdl.handle.net/20.500.11769/241616 | |
| Appare nelle tipologie: | 1.1 Articolo in rivista |
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http://hdl.handle.net/20.500.11769/241616
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