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Consider the following conditions. (a) Every regular LB-space is complete; (b) if an operator T between complete LB-spaces maps bounded sets into relatively compact sets, then T factorizes through a Montel LB-space; (c) for every complete LB-space E the space C (βℕ, E) is bornological. We show that (a) ⇒ (b) ⇒ (c). Moreover, we show that if E is Montel, then (c) holds. An example of an LB-space E with a strictly increasing transfinite sequence of its Mackey derivatives is given.

Factorization of operators on C*-algebras

Narcisse Randrianantoanina (1998)

Studia Mathematica

Let A be a C*-algebra. We prove that every absolutely summing operator from A into $ℓ_{2}$ factors through a Hilbert space operator that belongs to the 4-Schatten-von Neumann class. We also provide finite-dimensional examples that show that one cannot replace the 4-Schatten-von Neumann class by the p-Schatten-von Neumann class for any p < 4. As an application, we show that there exists a modulus of capacity ε → N(ε) so that if A is a C*-algebra and $T \in Π_{1} (A, ℓ_{2})$ with $π_{1} (T) \leq 1$ , then for every ε >0, the ε-capacity of...

Factorization of vector measures and their integration operators

José Rodríguez (2016)

Colloquium Mathematicae

Let X be a Banach space and ν a countably additive X-valued measure defined on a σ-algebra. We discuss some generation properties of the Banach space L¹(ν) and its connection with uniform Eberlein compacta. In this way, we provide a new proof that L¹(ν) is weakly compactly generated and embeds isomorphically into a Hilbert generated Banach space. The Davis-Figiel-Johnson-Pełczyński factorization of the integration operator $I_{ν} : L ¹ (ν) \to X$ is also analyzed. As a result, we prove that if $I_{ν}$ is both completely continuous...

Factorization of weakly continuous holomorphic mappings

Manuel González, Joaqín Gutiérrez (1996)

Studia Mathematica

We prove a basic property of continuous multilinear mappings between topological vector spaces, from which we derive an easy proof of the fact that a multilinear mapping (and a polynomial) between topological vector spaces is weakly continuous on weakly bounded sets if and only if it is weakly uniformly} continuous on weakly bounded sets. This result was obtained in 1983 by Aron, Hervés and Valdivia for polynomials between Banach spaces, and it also holds if the weak topology is replaced by a coarser...

Factorization theorem for $1$ -summing operators

Irene Ferrando (2011)

Czechoslovak Mathematical Journal

We study some classes of summing operators between spaces of integrable functions with respect to a vector measure in order to prove a factorization theorem for $1$ -summing operators between Banach spaces.

Failure of the condition N below $W^{1, n}$ .

Kauhanen, Janne (2002)

Annales Academiae Scientiarum Fennicae. Mathematica

Faisceaux d'espaces de Sobolev et principes du minimum

Denis Feyel, A. de La Pradelle (1975)

Annales de l'institut Fourier

On montre que le faisceau $ℱ$ des sursolutions locales dans $W_{loc}^{2}$ d’un certain opérateur elliptique $L$ est maximal pour un principe du minimum adapté aux espaces de Sobolev. La continuité de la réduite variationnelle des éléments continus permet alors d’étudier des représentants s.c.i.

Familias compactas de funciones holomorfas con desarrollo asintótico en abierto de Cn.

Piedad Guijarro Carranza (1986)

Stochastica

Let U be an open convex subset of Cn, n belonging to N, such that the set of all polinomies is dense in the space of all holomorphic and complex functions on U, (H(U), t0), where t0 is the open-compact topology.We endow the space HK(U) of all holomorphic functions on U that have asymptotic expansion at the origin with a metric and we study a particular compact subset of HK(U).

Families of functions dominated by distributions of $C$ -classes of mappings

Goo Ishikawa (1983)

Annales de l'institut Fourier

A subsheaf of the sheaf $ℰ_{Ω}$ of germs $C^{\infty}$ functions over an open subset $Ω$ of $R^{n}$ is called a sheaf of sub $C^{\infty}$ function. Comparing with the investigations of sheaves of ideals of $ℰ_{Ω}$ , we study the finite presentability of certain sheaves of sub $C^{\infty}$ -rings. Especially we treat the sheaf defined by the distribution of Mather’s $𝒞$ -classes of a $C^{\infty}$ mapping.

In this article we prove the Fatou's Lemma and Lebesgue's Convergence Theorem [10].MML identifier: MESFUN10, version: 7.9.01 4.101.1015

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Facial Topologies for Subspaces of C(X).

Factoring Operators Through Banach Lattices Not Containing C(0, 1).

Factorisation des applications $Λ p$ -sommantes

Factorisation des isomorphies d’ordre des espaces $L^{p}$

Factorisation d'un opérateur différentiel, III

Factorization in some Fréchet algebras of differentiable functions

Factorization in the algebra of rapidly decreasing functions on $𝐑_{n}$

Factorization of compact operators and applications to the approximation problem

Factorization of Montel operators