The characterizations of upper approximation operators based on special coverings

Pei Wang; Qingguo Li

Displaying similar documents to “The characterizations of upper approximation operators based on special coverings”

Approximation of functions from $L^{p} {(ω ̃)}_{β}$ by linear operators of conjugate Fourier series

WŁodzimierz Łenski, Bogdan Szal (2011)

Banach Center Publications

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We show the results corresponding to some theorems of S. Lal and H. K. Nigam [Int. J. Math. Math. Sci. 27 (2001), 555-563] on the norm and pointwise approximation of conjugate functions and to the results of the authors [Acta Comment. Univ. Tartu. Math. 13 (2009), 11-24] also on such approximations.

Some duality results on bounded approximation properties of pairs

Eve Oja, Silja Treialt (2013)

Studia Mathematica

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The main result is as follows. Let X be a Banach space and let Y be a closed subspace of X. Assume that the pair $(X *, Y^{⊥})$ has the λ-bounded approximation property. Then there exists a net $(S_{α})$ of finite-rank operators on X such that $S_{α} (Y) \subset Y$ and $| | S_{α} | | \leq λ$ for all α, and $(S_{α})$ and $(S *_{α})$ converge pointwise to the identity operators on X and X*, respectively. This means that the pair (X,Y) has the λ-bounded duality approximation property.

The polynomial approximation of continuous functions defined on $(- \infty, \infty)$

Leetsch C. Hsu (1959)

Czechoslovak Mathematical Journal

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Best approximation in spaces of bounded linear operators

Grzegorz Lewicki

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CONTENTSChapter 0...............................................................................................................................................................................5 0.1. Introduction..................................................................................................................................................................5 0.2. Preliminary results.......................................................................................................................................................9Chapter...

Compact operators whose adjoints factor through subspaces of $l_{p}$

Deba P. Sinha, Anil K. Karn (2002)

Studia Mathematica

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For p ≥ 1, a subset K of a Banach space X is said to be relatively p-compact if $K \subset \sum_{n = 1}^{\infty} α ₙ x ₙ : α ₙ \in B a l l (l_{p^{'}})$ , where p’ = p/(p-1) and $x ₙ \in l_{p}^{s} (X)$ . An operator T ∈ B(X,Y) is said to be p-compact if T(Ball(X)) is relatively p-compact in Y. Similarly, weak p-compactness may be defined by considering $x ₙ \in l_{p}^{w} (X)$ . It is proved that T is (weakly) p-compact if and only if T* factors through a subspace of $l_{p}$ in a particular manner. The normed operator ideals $(K_{p}, κ_{p})$ of p-compact operators and $(W_{p}, ω_{p})$ of weakly p-compact operators, arising from these factorizations,...

Multiple summing operators on $l_{p}$ spaces

Dumitru Popa (2014)

Studia Mathematica

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We use the Maurey-Rosenthal factorization theorem to obtain a new characterization of multiple 2-summing operators on a product of $l_{p}$ spaces. This characterization is used to show that multiple s-summing operators on a product of $l_{p}$ spaces with values in a Hilbert space are characterized by the boundedness of a natural multilinear functional (1 ≤ s ≤ 2). We use these results to show that there exist many natural multiple s-summing operators $T : l_{4 / 3} \times l_{4 / 3} \to l ₂$ such that none of the associated linear operators...

On a proof of the boundedness and nuclearity of pseudodifferential operators in $R^{n}$

Jan A. Rempała (1990)

Annales Polonici Mathematici

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On the compact approximation property

Vegard Lima, Åsvald Lima, Olav Nygaard (2004)

Studia Mathematica

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We show that a Banach space X has the compact approximation property if and only if for every Banach space Y and every weakly compact operator T: Y → X, the space = S ∘ T: S compact operator on X is an ideal in = span(,T) if and only if for every Banach space Y and every weakly compact operator T: Y → X, there is a net $(S_{γ})$ of compact operators on X such that $s u p_{γ} | | S_{γ} T | | \leq | | T | |$ and $S_{γ} \to I_{X}$ in the strong operator topology. Similar results for dual spaces are also proved.

Regularity of domains of parameterized families of closed linear operators

Teresa Winiarska, Tadeusz Winiarski (2003)

Annales Polonici Mathematici

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The purpose of this paper is to provide a method of reduction of some problems concerning families $A_{t} = {(A (t))}_{t \in}$ of linear operators with domains ${(_{t})}_{t \in}$ to a problem in which all the operators have the same domain . To do it we propose to construct a family ${(Ψ_{t})}_{t \in}$ of automorphisms of a given Banach space X having two properties: (i) the mapping $t \mapsto Ψ_{t}$ is sufficiently regular and (ii) $Ψ_{t} () =_{t}$ for t ∈ . Three effective constructions are presented: for elliptic operators of second order with the Robin boundary condition...

The Embeddability of c₀ in Spaces of Operators

Ioana Ghenciu, Paul Lewis (2008)

Bulletin of the Polish Academy of Sciences. Mathematics

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Results of Emmanuele and Drewnowski are used to study the containment of c₀ in the space $K_{w *} (X *, Y)$ , as well as the complementation of the space $K_{w *} (X *, Y)$ of w*-w compact operators in the space $L_{w *} (X *, Y)$ of w*-w operators from X* to Y.

Lebesgue type points in strong (C,α) approximation of Fourier series

Włodzimierz Łenski, Bogdan Roszak (2011)

Banach Center Publications

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We present an estimation of the $H_{k ₀, k_{r}}^{q, α} f$ and $H_{λ, u}^{ϕ, α} f$ means as approximation versions of the Totik type generalization (see [5], [6]) of the result of G. H. Hardy, J. E. Littlewood. Some corollaries on the norm approximation are also given.

On subextension and approximation of plurisubharmonic functions with given boundary values

Hichame Amal (2014)

Annales Polonici Mathematici

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Our aim in this article is the study of subextension and approximation of plurisubharmonic functions in $_{χ} (Ω, H)$ , the class of functions with finite χ-energy and given boundary values. We show that, under certain conditions, one can approximate any function in $_{χ} (Ω, H)$ by an increasing sequence of plurisubharmonic functions defined on strictly larger domains.

$L_{\infty}$ -Convergence of Finite Element Approximation

J. A. Nitsche (1975)

Publications mathématiques et informatique de Rennes

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Absolutely continuous linear operators on Köthe-Bochner spaces

(2011)

Banach Center Publications

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Let E be a Banach function space over a finite and atomless measure space (Ω,Σ,μ) and let $(X, | | \cdot | |_{X})$ and $(Y, | | \cdot | |_{Y})$ be real Banach spaces. A linear operator T acting from the Köthe-Bochner space E(X) to Y is said to be absolutely continuous if $| | T (1_{A ₙ} f) {| |}_{Y} \to 0$ whenever μ(Aₙ) → 0, (Aₙ) ⊂ Σ. In this paper we examine absolutely continuous operators from E(X) to Y. Moreover, we establish relationships between different classes of linear operators from E(X) to Y.

Spaces of compact operators on $C (2^{} \times [0, α])$ spaces

Elói Medina Galego (2011)

Colloquium Mathematicae

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We classify, up to isomorphism, the spaces of compact operators (E,F), where E and F are the Banach spaces of all continuous functions defined on the compact spaces $2^{} \times [0, α]$ , the topological products of Cantor cubes $2^{}$ and intervals of ordinal numbers [0,α].

Interpolation by elementary operators

Bojan Magajna (1993)

Studia Mathematica

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Given two n-tuples $a = (a_{1}, . . ., a_{n})$ and $b = (b_{1}, . . ., b_{n})$ of bounded linear operators on a Hilbert space the question of when there exists an elementary operator E such that $E a_{j} = b_{j}$ for all j =1,...,n, is studied. The analogous question for left multiplications (instead of elementary operators) is answered in any C*-algebra A, as a consequence of the characterization of closed left A-submodules in $A^{n}$ .

A remark on the approximation theorems of Whitney and Carleman-Scheinberg

Michal Johanis (2015)

Commentationes Mathematicae Universitatis Carolinae

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We show that a $C^{k}$ -smooth mapping on an open subset of $ℝ^{n}$ , $k \in ℕ \cup {0, \infty}$ , can be approximated in a fine topology and together with its derivatives by a restriction of a holomorphic mapping with explicitly described domain. As a corollary we obtain a generalisation of the Carleman-Scheinberg theorem on approximation by entire functions.

Operator $e^{- λ s^{α}}$

A. Takači (1978)

Matematički Vesnik

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Linear combinations of partitions of unity with restricted supports

Christian Richter (2002)

Studia Mathematica

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Given a locally finite open covering of a normal space X and a Hausdorff topological vector space E, we characterize all continuous functions f: X → E which admit a representation $f = \sum_{C \in} a_{C} φ_{C}$ with $a_{C} \in E$ and a partition of unity $φ_{C} : C \in$ subordinate to . As an application, we determine the class of all functions f ∈ C(||) on the underlying space || of a Euclidean complex such that, for each polytope P ∈ , the restriction ${f |}_{P}$ attains its extrema at vertices of P. Finally, a class of extremal functions on the...

The natural linear operators $T * ⇝ T T^{(r)}$

J. Kurek, W. M. Mikulski (2003)

Colloquium Mathematicae

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For natural numbers n ≥ 3 and r a complete description of all natural bilinear operators $T * \times_{ℳ f ₙ} T^{(0, 0)} ⇝ T^{(0, 0)} T^{(r)}$ is presented. Next for natural numbers r and n ≥ 3 a full classification of all natural linear operators $T *_{| ℳ f ₙ} ⇝ T T^{(r)}$ is obtained.

Extension operators on balls and on spaces of finite sets

Antonio Avilés, Witold Marciszewski (2015)

Studia Mathematica

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We study extension operators between spaces of continuous functions on the spaces $σ ₙ (2^{X})$ of subsets of X of cardinality at most n. As an application, we show that if $B_{H}$ is the unit ball of a nonseparable Hilbert space H equipped with the weak topology, then, for any 0 < λ < μ, there is no extension operator $T : C (λ B_{H}) \to C (μ B_{H})$ .

Representing non-weakly compact operators

Manuel González, Eero Saksman, Hans-Olav Tylli (1995)

Studia Mathematica

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For each S ∈ L(E) (with E a Banach space) the operator R(S) ∈ L(E**/E) is defined by R(S)(x** + E) = S**x** + E(x** ∈ E**). We study mapping properties of the correspondence S → R(S), which provides a representation R of the weak Calkin algebra L(E)/W(E) (here W(E) denotes the weakly compact operators on E). Our results display strongly varying behaviour of R. For instance, there are no non-zero compact operators in Im(R) in the case of $L^{1}$ and C(0,1), but R(L(E)/W(E)) identifies isometrically...

Functions in $L_{p}$ -space and their approximations

P. Chandra (1988)

Matematički Vesnik

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