Pełnotekstowe zasoby PLDML oraz innych baz dziedzinowych są już dostępne w nowej Bibliotece Nauki.
Zapraszamy na https://bibliotekanauki.pl
Preferencje help
Polish version English version Język
Widoczny [Schowaj] Abstrakt
Liczba wyników

Znaleziono wyników: 12

Liczba wyników na stronie
first rewind previous Strona / 1 next fast forward last

Wyniki wyszukiwania

help Sortuj według:

help Ogranicz wyniki do:
first rewind previous Strona / 1 next fast forward last
1
Content available remote

Banach spaces with small Calkin algebras

100%
González M.
Banach Center Publications
|
2007
|
tom 75
|
nr 1
159-170
EN
Let X be a Banach space. Let 𝓐(X) be a closed ideal in the algebra ℒ(X) of the operators acting on X. We say that ℒ(X)/𝓐(X) is a Calkin algebra whenever the Fredholm operators on X coincide with the operators whose class in ℒ(X)/𝓐(X) is invertible. Among other examples, we have the cases in which 𝓐(X) is the ideal of compact, strictly singular, strictly cosingular and inessential operators, and some other ideals introduced as perturbation classes in Fredholm theory. Our aim is to present some classes of Banach spaces and some concrete examples of Banach spaces for which some of their Calkin algebras are "small" in some sense: finite dimensional, commutative, etc. The first example of such a Banach space was constructed around 1990. However, at this moment there is a great variety of examples of spaces of this kind, which provides interesting examples and counterexamples of operators. Moreover, the methods and techniques of operator theory have been found to be useful in the study of these spaces.
2
Content available remote

Operational quantities characterizing semi-Fredholm operators

64%
González M., Martinón A.
Studia Mathematica
|
1995
|
tom 114
|
nr 1
13-27
EN
Several operational quantities have appeared in the literature characterizing upper semi-Fredholm operators. Here we show that these quantities can be divided into three classes, in such a way that two of them are equivalent if they belong to the same class, and are comparable and not equivalent if they belong to different classes. Moreover, we give a similar classification for operational quantities characterizing lower semi-Fredholm operators.
3
Content available remote

Local dual spaces of a Banach space

64%
González M., Martínez-Abejón A.
Studia Mathematica
|
2001
|
tom 147
|
nr 2
155-168
EN
We study the local dual spaces of a Banach space X, which can be described as the subspaces of X* that have the properties that the principle of local reflexivity attributes to X as a subspace of X**. We give several characterizations of local dual spaces, which allow us to show many examples. Moreover, every separable space X has a separable local dual Z, and we can choose Z with the metric approximation property if X has it. We also show that a separable space containing no copies of ℓ₁ admits a smallest local dual.
4
Content available remote

Factorization of weakly continuous holomorphic mappings

64%
González M., Gutiérrez J. M.
Studia Mathematica
|
1996
|
tom 118
|
nr 2
117-133
EN
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 one. However, we show that it need not be true for a stronger topology, thus answering a question raised by Aron. As an application of the first result, we prove that a holomorphic mapping ƒ between complex Banach spaces is weakly uniformly continuous on bounded subsets if and only if it admits a factorization of the form f = g∘S, where S is a compact operator and g a holomorphic mapping.
5
Content available remote

Calkin algebras for Banach spaces with finitely decomposable quotients

64%
González M., Herrera J.
Studia Mathematica
|
2003
|
tom 157
|
nr 3
279-293
EN
For a Banach space X such that all quotients only admit direct decompositions with a number of summands smaller than or equal to n, we show that every operator T on X can be identified with an n × n scalar matrix modulo the strictly cosingular operators SC(X). More precisely, we obtain an algebra isomorphism from the Calkin algebra L(X)/SC(X) onto a subalgebra of the algebra of n × n scalar matrices which is triangularizable when X is indecomposable. From this fact we get some information on the class of all semi-Fredholm operators on X and on the essential spectrum of an operator acting on X.
6
Content available remote

Decompositions for real Banach spaces with small spaces of operators

64%
González M., Herrera J.
Studia Mathematica
|
2007
|
tom 183
|
nr 1
1-14
EN
We consider real Banach spaces X for which the quotient algebra 𝓛(X)/ℐn(X) is finite-dimensional, where ℐn(X) stands for the ideal of inessential operators on X. We show that these spaces admit a decomposition as a finite direct sum of indecomposable subspaces $X_{i}$ for which $𝓛(X_{i})/ℐn(X_{i})$ is isomorphic as a real algebra to either the real numbers ℝ, the complex numbers ℂ, or the quaternion numbers ℍ. Moreover, the set of subspaces $X_{i}$ can be divided into subsets in such a way that if $X_{i}$ and $X_{j}$ are in different subsets, then $𝓛(X_{i},X_{j}) = ℐn(X_{i},X_{j})$; and if they are in the same subset, then $X_{i}$ and $X_{j}$ are isomorphic, up to a finite-dimensional subspace. Moreover, denoting by X̂ the complexification of X, we show that 𝓛(X)/ℐn(X) and 𝓛(X̂)/ℐn(X̂) have the same dimension.
7
Content available remote

On inessential and improjective operators.

64%
Aiena P., González M.
Studia Mathematica
|
1998
|
tom 131
|
nr 3
271-287
EN
We give several characterizations of the improjective operators, introduced by Tarafdar, and we characterize the inessential operators among the improjective operators. It is an interesting problem whether both classes of operators coincide in general. A positive answer would provide, for example, an intrinsic characterization of the inessential operators. We give several equivalent formulations of this problem and we show that the inessential operators acting between certain pairs of Banach spaces coincide with the improjective operators.
8
Content available remote

On incomparability of Banach spaces

64%
González M., Martinón A.
Banach Center Publications
|
1994
|
tom 30
|
nr 1
161-174
EN
Several concepts of incomparability of Banach spaces have been considered in the literature, which allow one to describe some of the properties of the product of two Banach spaces as a juxtaposition of the corresponding properties of the factors. In this paper we study the relations between these concepts of incomparability, survey the main results and applications, and state some open problems.
9
Content available remote

On nested sequences of convex sets in Banach spaces

52%
Castillo J., González M., Papini P.
Studia Mathematica
|
2014
|
tom 222
|
nr 1
19-28
EN
We study different aspects of the representation of weak*-compact convex sets of the bidual X** of a separable Banach space X via a nested sequence of closed convex bounded sets of X.
10
Content available remote

Representing non-weakly compact operators

52%
González M., Saksman E., Tylli H.-O.
Studia Mathematica
|
1995
|
tom 113
|
nr 3
265-282
EN
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 with the class of lattice regular operators on $ℓ^2$ for $E = ℓ^2(J)$ (here J is James' space). Accordingly, there is an operator $T ∈ L(ℓ^2(J))$ such that R(T) is invertible but T fails to be invertible modulo $W(ℓ^2(J))$.
11
Content available remote

Operators with an ergodic power

52%
Bermúdez T., González M., Mbekhta M.
Studia Mathematica
|
2000
|
tom 141
|
nr 3
201-208
EN
We prove that if some power of an operator is ergodic, then the operator itself is ergodic. The converse is not true.
12
Content available remote

On ultrapowers of Banach spaces of type $ℒ_{∞}$

45%
Avilés A., Cabello Sánchez F., Castillo J., González M., Moreno Y.
Fundamenta Mathematicae
|
2013
|
tom 222
|
nr 3
195-212
EN
We prove that no ultraproduct of Banach spaces via a countably incomplete ultrafilter can contain c₀ complemented. This shows that a "result" widely used in the theory of ultraproducts is wrong. We then amend a number of results whose proofs have been infected by that statement. In particular we provide proofs for the following statements: (i) All M-spaces, in particular all C(K)-spaces, have ultrapowers isomorphic to ultrapowers of c₀, as also do all their complemented subspaces isomorphic to their square. (ii) No ultrapower of the Gurariĭ space can be complemented in any M-space. (iii) There exist Banach spaces not complemented in any C(K)-space having ultrapowers isomorphic to a C(K)-space.
first rewind previous Strona / 1 next fast forward last
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.