تقرير
A note on smooth rotund norms which are not midpoint locally uniformly rotund
العنوان: | A note on smooth rotund norms which are not midpoint locally uniformly rotund |
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المؤلفون: | De Bernardi, Carlo Alberto, Preti, Alessandro, Somaglia, Jacopo |
سنة النشر: | 2024 |
المجموعة: | Mathematics |
مصطلحات موضوعية: | Mathematics - Functional Analysis |
الوصف: | We prove that every separable infinite-dimensional Banach space admits a G\^ateaux smooth and rotund norm which is not midpoint locally uniformly rotund. Moreover, by using a similar technique, we provide in every infinite-dimensional Banach space with separable dual a Fr\'echet smooth and weakly uniformly rotund norm which is not midpoint locally uniformly rotund. These two results provide a positive answer to some open problems by A. J. Guirao, V. Montesinos, and V. Zizler. |
نوع الوثيقة: | Working Paper |
URL الوصول: | http://arxiv.org/abs/2402.13869 |
رقم الأكسشن: | edsarx.2402.13869 |
قاعدة البيانات: | arXiv |
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