کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
5774652 | 1413564 | 2018 | 12 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
On the norm attainment set of a bounded linear operator
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
آنالیز ریاضی
چکیده انگلیسی
In this paper we explore the properties of a bounded linear operator defined on a Banach space, in light of operator norm attainment. Using Birkhoff-James orthogonality techniques, we give a necessary condition for a nonzero bounded linear operator to attain norm at a particular point of the unit sphere. We prove four corollaries to establish the importance of our study. As part of our exploration, we also obtain a characterization of smooth Banach spaces in terms of operator norm attainment and Birkhoff-James orthogonality. Restricting our attention to lp2(pâNâ{1}) spaces, we obtain an upper bound for the number of points at which any linear operator, which is not a scalar multiple of an isometry, may attain norm.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Mathematical Analysis and Applications - Volume 457, Issue 1, 1 January 2018, Pages 67-76
Journal: Journal of Mathematical Analysis and Applications - Volume 457, Issue 1, 1 January 2018, Pages 67-76
نویسندگان
Debmalya Sain,