Addendum to "Lineability and spaceability of vector-measure spaces" (Studia Math. 219 (2013), 155-161)
Giuseppina Barbieri, Francisco J. García-Pacheco, Daniele Puglisi (2014)
Studia Mathematica
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Displaying similar documents to “Bounded sets in the range of -valued measure with bounded variation.”
Addendum to "Lineability and spaceability of vector-measure spaces" (Studia Math. 219 (2013), 155-161)
Compactness of the integration operator associated with a vector measure
S. Okada, W. J. Ricker, L. Rodríguez-Piazza (2002)
Studia Mathematica
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A characterization is given of those Banach-space-valued vector measures m with finite variation whose associated integration operator Iₘ: f ↦ ∫fdm is compact as a linear map from L¹(m) into the Banach space. Moreover, in every infinite-dimensional Banach space there exist nontrivial vector measures m (with finite variation) such that Iₘ is compact, and other m (still with finite variation) such that Iₘ is not compact. If m has infinite variation, then Iₘ is never compact.
Derivability, variation and range of a vector measure
L. Rodríguez-Piazza (1995)
Studia Mathematica
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We prove that the range of a vector measure determines the σ-finiteness of its variation and the derivability of the measure. Let F and G be two countably additive measures with values in a Banach space such that the closed convex hull of the range of F is a translate of the closed convex hull of the range of G; then F has a σ-finite variation if and only if G does, and F has a Bochner derivative with respect to its variation if and only if G does. This complements a result of [Ro] where...
Some remarks on an operator equation in a Banach space
Bogdan Rzepecki (1980)
Annales Polonici Mathematici
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Operator ideal properties of vector measures with finite variation
Susumu Okada, Werner J. Ricker, Luis Rodríguez-Piazza (2011)
Studia Mathematica
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Given a vector measure m with values in a Banach space X, a desirable property (when available) of the associated Banach function space L¹(m) of all m-integrable functions is that L¹(m) = L¹(|m|), where |m| is the [0,∞]-valued variation measure of m. Closely connected to m is its X-valued integration map Iₘ: f ↦ ∫f dm for f ∈ L¹(m). Many traditional operators from analysis arise as integration maps in this way. A detailed study is made of the connection between the property L¹(m) = L¹(|m|)...
Nonseparability of the quotient space cabv(∑,m;X)/L¹(m;X) for Banach spaces X without the Radon-Nikodym property
Lech Drewnowski (1993)
Studia Mathematica
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It is shown that if (S,∑,m) is an atomless finite measure space and X is a Banach space without the Radon-Nikodym property, then the quotient space cabv(∑,m;X)/L¹(m;X) is nonseparable.
Banach-Stone theorems for non-separably valued Bochner – spaces
Greim, Peter
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Three Spaces Problem for Lyapunov Theorem on Vector Measure
Kadets, V., Vladimirskaya, O. (1998)
Serdica Mathematical Journal
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It is proved that a Banach space X has the Lyapunov property if its subspace Y and the quotient space X/Y have it.
Conical measures and properties of a vector measure determined by its range
L. Rodríguez-Piazza, M. Romero-Moreno (1997)
Studia Mathematica
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We characterize some properties of a vector measure in terms of its associated Kluvánek conical measure. These characterizations are used to prove that the range of a vector measure determines these properties. So we give new proofs of the fact that the range determines the total variation, the σ-finiteness of the variation and the Bochner derivability, and we show that it also determines the (p,q)-summing and p-nuclear norm of the integration operator. Finally, we show that Pettis derivability...
On the generalized continuity of the semivariation in locally convex spaces
Ján Haluška (1991)
Acta Universitatis Carolinae. Mathematica et Physica
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