Factorization of compact operators and applications to the approximation problem
Factorization of Montel operators
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
Let A be a C*-algebra. We prove that every absolutely summing operator from A into 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 with , then for every ε >0, the ε-capacity of...
Factorization of vector measures and their integration operators
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 is also analyzed. As a result, we prove that if is both completely continuous...
Factorization of weakly continuous holomorphic mappings
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 -summing operators
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 -summing operators between Banach spaces.
Failure of the condition N below .
Faisceaux d'espaces de Sobolev et principes du minimum
On montre que le faisceau des sursolutions locales dans d’un certain opérateur elliptique 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.
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 -classes of mappings
A subsheaf of the sheaf of germs functions over an open subset of is called a sheaf of sub function. Comparing with the investigations of sheaves of ideals of , we study the finite presentability of certain sheaves of sub -rings. Especially we treat the sheaf defined by the distribution of Mather’s -classes of a mapping.
Familles absolument sommables et propriété de Radon-Nikodym
Fastautomorphe Funktionen auf komplexen Räumen.
Fatou's Lemma and the Lebesgue's Convergence Theorem
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
Feller semigroups obtained by variable order subordination.
Fenchel-Orlicz spaces [Book]
FF-Banachverbandsalgebren.
Filters and sequences
We consider two situations which relate properties of filters with properties of the limit operators with respect to these filters. In the first one, we show that the space of sequences having limits with respect to a filter is itself and therefore, by a result of Dobrowolski and Marciszewski, such spaces are topologically indistinguishable. This answers a question of Dobrowolski and Marciszewski. In the second one, we characterize universally measurable filters which fulfill Fatou’s lemma.
Fine behavior of functions whose gradients are in an Orlicz space
For functions whose derivatives belong to an Orlicz space, we develop their "fine" properties as a generalization of the treatment found in [MZ] for Sobolev functions. Of particular importance is Theorem 8.8, which is used in the development in [MSZ] of the coarea formula for such functions.
Fine topology of variable exponent energy superminimizers.
Finite codimensional linear isometries on spaces of differentiable and Lipschitz functions
We characterize finite codimensional linear isometries on two spaces, C (n)[0; 1] and Lip [0; 1], where C (n)[0; 1] is the Banach space of n-times continuously differentiable functions on [0; 1] and Lip [0; 1] is the Banach space of Lipschitz continuous functions on [0; 1]. We will see they are exactly surjective isometries. Also, we show that C (n)[0; 1] and Lip [0; 1] admit neither isometric shifts nor backward shifts.