Results 311 to 320 of about 10,024,030 (363)

E-approximation properties

Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 2020
A Banach space \(X\) has the approximation property (AP) if the identity map of \(X\) can be approximated by finite rank operators over compact sets [\textit{A.~Grothendieck}, Produits tensoriels topologiques et espaces nucléaires. Providence, RI: American Mathematical Society (AMS) (1955; Zbl 0064.35501)].
Ju Myung Kim, Bentuo Zheng
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The approximation property for spaces of Lipschitz functions with the bounded weak* topology

Revista matemática iberoamericana, 2018
Let X be a pointed metric space and let Lip0(X) be the space of all scalar-valued Lipschitz functions on X which vanish at the base point. We prove that Lip0(X) with the bounded weak* topology τbw∗ has the approximation property if and only if the ...
A. Jiménez-Vargas
semanticscholar   +1 more source

Bounded Approximation Properties

2005
Throughout this section let X be a separable Banach space. We investigate certain approximation properties for X and deal with the question under which additional condition then X has a basis. In this context we also give a sufficient criterion for X to be a dual Banach space.
Vladimir I. Gurariy, Wolfgang Lusky
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Approximation properties for KAC algebras

Indiana University Mathematics Journal, 1999
It is well known that a locally compact group \(G\) is amenable if and only if its Fourier algebra \(A(G)\) has a bounded approximate identity. A locally compact group \(G\) is said to be weakly amenable if there is an approximate identity \((u_i)\) for \(A(G)\) such that the corresponding multipliers \(m_{u_i}\) satisfy \(\sup\|m_{u_i}\|_{cb}
Kraus, Jon, Ruan, Zhong-Jin
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Universal Approximation Capability of Broad Learning System and Its Structural Variations

IEEE Transactions on Neural Networks and Learning Systems, 2019
After a very fast and efficient discriminative broad learning system (BLS) that takes advantage of flatted structure and incremental learning has been developed, here, a mathematical proof of the universal approximation property of BLS is provided.
Ieee C. L. Philip Chen Fellow, Zhulin Liu, Shuang Feng   +2 more
semanticscholar   +1 more source

On the bounded approximation property in Banach spaces

, 2013
We prove that the kernel of a quotient operator from an L1-space onto a Banach space X with the Bounded Approximation Property (BAP) has the BAP. This completes earlier results of Lusky-case ℓ1-and Figiel, Johnson and Pełczyński-case X* separable.
J. Castillo, Yolanda Moreno
semanticscholar   +1 more source

The Approximation Property

2002
In this chapter we introduce the approximation property for Banach spaces. The possession of this property leads to the resolution of several outstanding issues concerning projective and injective tensor products. We then consider the following question: when are the projective or injective tensor products of reflexive spaces themselves reflexive?
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The Approximation Property

1981
Roughly speaking, the approximation problem is the question if it is true, for a given lcs E, that every operator in L (E, E) can be approximated by finite rank operators, uniformly on compact sets. If E is a Banach space, then this is equivalent to asking whether every compact operator from any Banach space with values in E can be approximated by ...
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Borel cocycles, approximation properties and relative property T

Ergodic Theory and Dynamical Systems, 2000
Let $G$ and $H$ be locally compact groups. Assume that $G$ acts on a standard probability space $(S,\mu)$, $\mu$ being $G$-invariant. We prove that if there exists a Borel cocycle $\alpha:S\times G\longrightarrow H$ which is proper in an appropriate sense, then $G$ inherits some approximation properties of $H$, for instance amenability or the so-called
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On Saphar’s Approximation Property of Order p and the $$w_p$$-Approximation Property

Mediterranean Journal of Mathematics
Let \(1\le p\le \infty\). A Banach space \(X\) is said to have the \(g_p\)-approximation property (the \(g_p\)-AP) if the natural mapping \(Y\widehat{\otimes}_{g_p} X\to Y\widehat{\otimes}_\varepsilon X\) is injective for all Banach spaces \(Y\). Here \(Y\widehat{\otimes}_{g_p} X\) denotes the completion of the tensor product \(Y\otimes X\) in the ...
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