کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4613990 | 1339277 | 2017 | 7 صفحه PDF | دانلود رایگان |
We 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.
Journal: Journal of Mathematical Analysis and Applications - Volume 445, Issue 2, 15 January 2017, Pages 1321–1327