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The Compact Approximation Property does not imply the Approximation Property [PDF]
Studia Mathematica, 1992 It is shown how to construct, given a Banach space which does not have the approximation property, another Banach space which does not have the approximation property but which does have the compact approximation ...
Willis, George A.
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An approximation property of Gaussian functions [PDF]
Electronic Journal of Differential Equations, 2013 Using the power series method, we solve the inhomogeneous linear first order differential equation $$ y'(x) + lambda (x-mu) y(x) = sum_{m=0}^infty a_m (x-mu)^m, $$ and prove an approximation property of Gaussian functions.
Soon-Mo Jung +2 more
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Domains via approximation operators [PDF]
Logical Methods in Computer Science, 2018 In this paper, we tailor-make new approximation operators inspired by rough set theory and specially suited for domain theory. Our approximation operators offer a fresh perspective to existing concepts and results in domain theory, but also reveal ways ...
Zhiwei Zou, Qingguo Li, Weng Kin Ho
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An Approximation Property of Pisot Numbers
Journal of Number Theory, 2000 Given a positive real number \(q\) and an integer \(m\geq 1\), denote by \(\Lambda= \Lambda_m\) the set of all real numbers \(y\) having at least one representation of the form \[ y= \varepsilon_0+ \varepsilon_1q+ \varepsilon_2 q^2+\cdots+ \varepsilon_n q^n \] with some integer \(n> 0\) and \(\varepsilon_i\in \{-m, -m+1,\dots, -1,0,1,\dots, m-1,m ...
Vilmos Komornik +2 more
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Approximation properties for dual spaces
MATHEMATICA SCANDINAVICA, 2003 We prove that a Banach space $X$ has the metric approximation property if and only if $\mathcal F(Y,X)$ is an ideal in $\mathcal L(Y,X^{**})$ for all Banach spaces $Y$. Furthermore, $X^*$ has the metric approximation property if and only if for all Banach spaces $Y$ and all Hahn-Banach extension operators $\phi : X^* \rightarrow X^{***}$ there exists a
Vegard Lima
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The tight approximation property
Journal für die reine und angewandte Mathematik (Crelles Journal), 2021 AbstractThis article introduces and studies the tight approximation property, a property of algebraic varieties defined over the function field of a complex or real curve that refines the weak approximation property (and the known cohomological obstructions to it) by incorporating an approximation condition in the Euclidean topology.
Olivier Wittenberg +3 more
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The Approximation Property Does Not Imply the Bounded Approximation Property [PDF]
Proceedings of the American Mathematical Society, 1973 There is a Banach space which has the approxi- mation property but fails the bounded approximation property. The space can be chosen to have separable conjugate, hence there is a nonnuclear operator on the space which has nuclear adjoint. This latter result solves a problem of Grothendieck (2).
T. Figiel, William B. Johnson
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History, Developments and Open Problems on Approximation Properties
Mathematics, 2020 In this paper, we give a comprehensive review of the classical approximation property. Then, we present some important results on modern variants, such as the weak bounded approximation property, the strong approximation property and p-approximation ...
Ju Myung Kim, Bentuo Zheng
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A Study of Spaces of Sequences in Fuzzy Normed Spaces
Mathematics, 2021 In this paper, spaces of sequences in fuzzy normed spaces are considered. These spaces are a new concept in fuzzy normed spaces. We develop fuzzy norms for spaces of sequences in fuzzy normed spaces. Especially, we study the representation of the dual of
Ju-Myung Kim, Keun-Young Lee
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On the compact approximation property [PDF]
Studia Mathematica, 2004 A Banach space \(X\) is said to have the approximation property if its identity operator can be uniformly approximated on compact subsets of \(X\) by finite-rank operators. If the identity is allowed to be approximated by compact operators (instead of finite-rank operators), then \(X\) is said to have the compact approximation property (C.A.P.
Olav Nygaard, Åsvald Lima, Vegard Lima
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