کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
8900023 | 1631554 | 2018 | 23 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Closedness of the set of extreme points of the unit ball in Orlicz spaces equipped with the p-Amemiya norm
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
آنالیز ریاضی
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چکیده انگلیسی
It is known (see the classical book “Linear Operators I” by N. Dunford and J.T. Schwarz [6]) that compact nice operators from a Banach space X into the space of continuous functions C(Z,R) are extreme points of the unit ball of compact operators B(K(X,C(Z,R))), where Z is a compact Hausdorff space. Recall, that an operator T is called nice if Tâ(Z)âExtB(X), where the continuous mapping Tâ is defined by Tâ(z)(x)=T(x)(z) for all xâX and zâZ. It is evident that if the set ExtB(X) is closed, then T is nice if and only if Tâ(Z0)âExtB(X) on a dense subset Z0âZ. In general the set of extreme points ExtB(X) need not to be closed. In 1992 A. Suarez-Granero and M. WisÅa presented the criteria for closedness of the set of extreme points of the unit ball in the case of Orlicz spaces equipped with the Luxemburg norm. The aim of this paper is to present the criteria for the closedness of the set of extreme points of the unit ball for the wide class of norms - the so-called p-Amemiya norms. This class includes both the Orlicz and the Luxemburg norm. The Orlicz functions that generates Orlicz spaces are assumed to be as much general as possible, in particular the Orlicz functions can vanish outside zero and jump to infinity what follows that the investigated Orlicz spaces can contain isomorphic copy of Lâ or be a subspace of Lâ.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Mathematical Analysis and Applications - Volume 461, Issue 1, 1 May 2018, Pages 378-400
Journal: Journal of Mathematical Analysis and Applications - Volume 461, Issue 1, 1 May 2018, Pages 378-400
نویسندگان
Marek WisÅa,