کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4590833 | 1334987 | 2013 | 41 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Stability of vector measures and twisted sums of Banach spaces
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
![عکس صفحه اول مقاله: Stability of vector measures and twisted sums of Banach spaces Stability of vector measures and twisted sums of Banach spaces](/preview/png/4590833.png)
چکیده انگلیسی
A Banach space X is said to have the SVM (stability of vector measures) property if there exists a constant v<â such that for any algebra of sets F, and any function ν:FâX satisfyingâν(AâªB)âν(A)âν(B)â⩽1for disjoint A,BâF, there is a vector measure μ:FâX with âν(A)âμ(A)â⩽v for all AâF. If this condition is valid when restricted to set algebras F of cardinality less than some fixed cardinal number κ, then we say that X has the κ-SVM property. The least cardinal κ for which X does not have the κ-SVM property (if it exists) is called the SVM character of X. We apply the machinery of twisted sums and quasi-linear maps to characterise these properties and to determine SVM characters for many classical Banach spaces. We also discuss connections between the κ-SVM property, κ-injectivity and the 'three-space' problem.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Functional Analysis - Volume 264, Issue 10, 15 May 2013, Pages 2416-2456
Journal: Journal of Functional Analysis - Volume 264, Issue 10, 15 May 2013, Pages 2416-2456
نویسندگان
Tomasz Kochanek,