کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
9502721 1339538 2005 10 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Extreme points of Banach lattices related to conditional expectations
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آنالیز ریاضی
پیش نمایش صفحه اول مقاله
Extreme points of Banach lattices related to conditional expectations
چکیده انگلیسی
Let (X,F,μ) be a complete probability space, B a sub-σ-algebra, and Φ the probabilistic conditional expectation operator determined by B. Let K be the Banach lattice {f∈L1(X,F,μ):‖Φ(|f|)‖∞<∞} with the norm ‖f‖=‖Φ(|f|)‖∞. We prove the following theorems:(1)The closed unit ball of K contains an extreme point if and only if there is a localizing set E for B such that supp(Φ(χE))=X.(2)Suppose that there is n∈N such that f⩽nΦ(f) for all positive f in L∞(X,F,μ). Then K has the uniformly λ-property and every element f in the complex K with ‖f‖⩽1n is a convex combination of at most 2n extreme points in the closed unit ball of K.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Mathematical Analysis and Applications - Volume 312, Issue 1, 1 December 2005, Pages 138-147
نویسندگان
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