Results 111 to 120 of about 3,701 (139)

Fixed points in the nonstandard hull of a Banach space

Nonlinear Analysis: Theory, Methods & Applications, 1998
This article presents some results on fixed points for nonexpansive mappings on the base of methods of nonstandard analysis. First, the well-known result about the existence of almost fixed points for nonexpansive selfmaps of a bounded closed convex set is reformulated by the authors as the statement that each liftable nonexpansive selfmap \(f\) on a ...
Baratella, Stefano, S. A. Ng
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Spectral theory of group representations and their nonstandard hull

Israel Journal of Mathematics, 1984
Let G denote a locally compact abelian group and let U be a bounded strongly continuous representation of G on the Banach space E. We introduce the notion of the Riesz part \(R\sigma\) (U) of the Arveson spectrum \(\sigma\) (U) of U. The representation U is called R-compact if every bounded subset \(C\subset E\) satisfying \(\lim_{t\to e}\sup \{\| U_ ...
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Nonstandard hulls of unbounded symmetric operators

Siberian Mathematical Journal, 1998
If \(E\) is an internal normed space, \(E^{\sharp}\) is its nonstandard hull, and \(A\: E\to E\) is an internal linear operator with limited norm then there exists a well-defined operator \(A^{\sharp}\: E^{\sharp}\to E^{\sharp}\) called the nonstandard hull of \(A\). The principal difficulty arises for \(A\) with unlimited norm.
Gordon, E. I., Zdorovenko, M. Yu.
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On Nonstandard Hulls of Convex Spaces

Canadian Journal of Mathematics, 1976
A nonstandard hull of a TVS (locally convex topological vector space) is a standard TVS constructed from a nonstandard model for [3]. If the nonstandard hulls of a TVS are independent of the non-standard model, we say that the TVS has invariant nonstandard hulls. This is (for complete spaces) the property that every finite element is inflnitesimally
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Nonstandard hulls of Banach spaces

Israel Journal of Mathematics, 1976
The main theme of this paper is the relationship between a Banach spaceE and its nonstandard hullsE (including ultrapowers ofE). Emphasis is placed on the ways in which the general structure ofE is determined by the approximate shape and arrangement of the finite dimensional subspaces ofE.
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Nonstandard hulls of vector lattices

Siberian Mathematical Journal, 1994
The author defines the nonstandard hull \(\overline E\) of a vector lattice \(E\) in an analogous way to the usual definition of the nonstandard hull \(\widetilde V\) of a normed vector space \(V\), whereas the absolute value on \(E\) replaces the role of the norm on \(V\). For a normed vector lattice \(E\), he compares \(\overline E\) and \(\widetilde
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A remark on uniform spaces with invariant nonstandard hulls

MLQ, 2005
Let \(X\) be a uniform space with its uniformity generated by a set of pseudo-metrics \(\Gamma \). Let the symbol \(\simeq \) denote the infinitesimal relation on the nonstandard extension \(^{\ast }X,\) where \(x\simeq y\) means that \(^{\ast }\rho \left( x,y\right) \) is infinitesimal to \(0\) for each \( \rho \in \Gamma .\) This equivalence relation
Vakil, Nader, Vakil, Roozbeh
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Nonstandard hulls of Lebesgue-Bochner spaces

1995
The problem of finding a representation of the nonstandard hull of L p (μ, E) for 1 ≤ p ∞ (E a Banach space) was posed by Henson and Moore in 1983 (see [3]). A related question was, whether this nonstandard hull can be described in some smooth way in terms of only (Math) and E. We show that the answer to this question is negative.
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When do two Banach spaces have isometrically isomorphic nonstandard hulls?

Israel Journal of Mathematics, 1975
The answer to the title question is given in terms of the elementary properties of Banach spaces regarded as structures for a certain first-order language. The same question for Banach space ultrapowers is also considered. The connection between nonstandard hulls and Banach space ultrapowers derives in part from the following fact, of independent ...
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Representation of Nonstandard Hulls in IST for Certain Uniform Spaces

Mathematical Logic Quarterly, 1991
Suppose that \((X,D)\) is an admissible Hausdorff uniform space, where \(X\) is an infinite set and \(D\) is a standard family of pseudo-metrics on \(X\) that yields the Hausdorff uniform structure. The author defines three standard subsets \(X_ 0,X_ 1,\hat X\) of the set of all real valued functions defined in \(X\times D\), where \(X_ 0\subset X_ 1 ...
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