کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4613990 1339277 2017 7 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Renormings concerning the lineability of the norm-attaining functionals
ترجمه فارسی عنوان
نرم‌سازی مجدد مربوط به قابلیت خطی بودن فانکشنال های تحقق نرم
کلمات کلیدی
قابلیت خطی بودن؛ فانکشنال تحقق نرم ؛ نرم‌سازی مجدد؛ نرم‌سازی ؛ Biorthogonal
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آنالیز ریاضی
چکیده انگلیسی

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.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Mathematical Analysis and Applications - Volume 445, Issue 2, 15 January 2017, Pages 1321–1327
نویسندگان
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