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• W2016604875 abstract "A Banach space X is said to have the SVM (stability of vector measures) property if there exists a constant v<∞ such that for any algebra of sets F, and any function ν:F→X satisfying‖ν(A∪B)−ν(A)−ν(B)‖⩽1for disjoint A,B∈F, there is a vector measure μ:F→X with ‖ν(A)−μ(A)‖⩽v for all A∈F. 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." @default.
• W2016604875 created "2016-06-24" @default.
• W2016604875 creator A5050220284 @default.
• W2016604875 date "2013-05-01" @default.
• W2016604875 modified "2023-10-18" @default.
• W2016604875 title "Stability of vector measures and twisted sums of Banach spaces" @default.
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• W2016604875 doi "https://doi.org/10.1016/j.jfa.2013.03.001" @default.
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