Displaying similar documents to “Stretched shadings and a Banach measure that is not scale-invariant”

On the generalized Avez method

Antoni Leon Dawidowicz (1992)

Annales Polonici Mathematici

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A generalization of the Avez method of construction of an invariant measure is presented.

Note on measures of noncompactness in Banach sequence spaces.

Jozef Banas, Antonio Martinón (1990)

Extracta Mathematicae

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The notion of a measure of noncompactness turns out to be a very important and useful tool in many branches of mathematical analysis. The current state of this theory and its applications are presented in the books [1,4,11] for example. The notion of a measure of weak noncompactness was introduced by De Blasi [8] and was subsequently used in numerous branches of functional analysis and the theory of differential and integral equations (cf. [2,3,9,10,11], for instance). ...

Lyapunov theorem for q-concave Banach spaces

Anna Novikova (2014)

Studia Mathematica

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A generalization of the Lyapunov convexity theorem is proved for a vector measure with values in a Banach space with unconditional basis, which is q-concave for some q < ∞ and does not contain any isomorphic copy of l₂.

Invariant Means on Banach Spaces

Radosław Łukasik (2017)

Annales Mathematicae Silesianae

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In this paper we study some generalization of invariant means on Banach spaces. We give some sufficient condition for the existence of the invariant mean and some examples where we have not it.

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.

Measures of noncompactness and normal structure in Banach spaces

J. García-Falset, A. Jiménez-Melado, E. Lloréns-Fuster (1994)

Studia Mathematica

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Sufficient conditions for normal structure of a Banach space are given. One of them implies reflexivity for Banach spaces with an unconditional basis, and also for Banach lattices.