کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4673360 | 1346631 | 2006 | 18 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
The de Schipper formula and squares of Riesz spaces
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات (عمومی)
پیش نمایش صفحه اول مقاله
![عکس صفحه اول مقاله: The de Schipper formula and squares of Riesz spaces The de Schipper formula and squares of Riesz spaces](/preview/png/4673360.png)
چکیده انگلیسی
In this paper we introduce and study the square mean and the geometric mean in Riesz spaces. We prove that every geometric mean closed Riesz space is square mean closed and give a counterexample to the converse. We define for positive a, b in a square mean closed Riesz space E an addition via the formulaa⊞b=sup {(cos x)a + (sin x)b: 0 ⩽ x ⩽ 2π},which goes back to a formula by de Schipper. In case that E is geometric mean closed this turns the mldeflying set of the positive cone of E into a lattice ordered semigroup, which in turn is the positive cone ofa Riesz space E□. We prove, under the additional condition that E is geometric mean closed, that E□ is Riesz isomorphic to the square of E as introduced earlier by Buskes and van Rooij.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Indagationes Mathematicae - Volume 17, Issue 4, 18 December 2006, Pages 479-496
Journal: Indagationes Mathematicae - Volume 17, Issue 4, 18 December 2006, Pages 479-496