Results 1 to 10 of about 10,024,030 (363)

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.
core   +3 more sources

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).
Figiel, T., Johnson, W. B.
openaire   +3 more sources

An approximation property of Gaussian functions

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, Hamdullah Sevli, Sebaheddin Sevgin   +2 more
doaj   +5 more sources

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
doaj   +1 more source

SAC Property and Approximate Semicontinuity [PDF]

Real Analysis Exchange, 2000
For a bounded measurable function \(f:{\mathcal R} \to {\mathcal R}\) and for real \(r > 0\) let \[ p_r(x) = \sup \left\{ s\in (0,1]:\biggl|\frac{1}{h}\int_x^{x+h}f(t) dt- f(x)\biggr|< r\;\text{for }0 < |h|< s\right\} . \] If in the above formula we write \(\leq r\) then we define \(q_r(x)\).
Prus-Wiśniowski, Franciszek, Szkibiel, Grzegorz   +1 more
openaire   +4 more sources

The K_p,q-Compactness and K_p,q-Null Sequences, and the ${\mathcal{K}}_{{\mathit{K}}_{\mathit{p},\mathit{q}}}$-Approximation Property for Banach Spaces

Mathematics, 2022
Let Kp,q (1≤p,q≤∞ with 1/p+1/q≥1) be the ideal of (p,q)-compact operators. This paper investigates the compactness and null sequences via Kp,q, and an approximation property of the ideal of Kp,q-compact operators.
Ju Myung Kim
doaj   +1 more source

A Study of Approximation Properties in Felbin-Fuzzy Normed Spaces

Mathematics, 2020
In this paper, approximation properties in Felbin-fuzzy normed spaces are studied. These approximation properties have been recently introduced in Felbin-fuzzy normed spaces. We make topological tools to analyze such approximation properties.
Ju Myung Kim, Keun Young Lee
doaj   +1 more source

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
doaj   +1 more source

Hereditary approximation property [PDF]

Annals of Mathematics, 2012
Let \(X\) be a Banach space. The authors say that \(X\) has the hereditary approximation property (HAP) or is an HAPpy space if all closed subspaces of \(X\) have the approximation property. Hilbert spaces are clearly HAPpy. The first HAPpy spaces which are not isomorphic to Hilbert spaces were constructed by \textit{W. B. Johnson} [Functional analysis,
Johnson, W. B., Szankowski, A.
openaire   +2 more sources

Body-Ordered Approximations of Atomic Properties [PDF]

Archive for Rational Mechanics and Analysis, 2022
AbstractWe show that the local density of states (LDOS) of a wide class of tight-binding models has a weak body-order expansion. Specifically, we prove that the resulting body-order expansion for analytic observables such as the electron density or the energy has an exponential rate of convergence both at finite Fermi-temperature as well as for ...
Jack Thomas, Huajie Chen, Christoph Ortner   +2 more
openaire   +2 more sources