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1
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Derivative and antiderivative operators and the size of complex domains

100%
Bernal-González L.
Annales Polonici Mathematici
|
1994
|
tom 59
|
nr 3
267-274
EN
We prove some conditions on a complex sequence for the existence of universal functions with respect to sequences of certain derivative and antiderivative operators related to it. These operators are defined on the space of holomorphic functions in a complex domain. Conditions for the equicontinuity of those sequences are also studied. The conditions depend upon the size of the domain.
2
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Disjoint hypercyclic operators

100%
Bernal-González L.
Studia Mathematica
|
2007
|
tom 182
|
nr 2
113-131
EN
We introduce the concept of disjoint hypercyclic operators. These are operators performing the approximation of any given vectors with a common subsequence of iterates applied on a common vector. The notion is extended to sequences of operators, and applied to composition operators and differential operators on spaces of analytic functions.
3
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Universal images of universal elements

100%
Bernal-González L.
Studia Mathematica
|
2000
|
tom 138
|
nr 3
241-250
EN
We furnish several necessary and sufficient conditions for the following property: For a topological space X, a continuous selfmapping S of X and a family τ of continuous selfmappings of X, the image under S of every τ-universal element is also τ-universal. An application in operator theory, where we extend results of Bourdon, Herrero, Bes, Herzog and Lemmert, is given. In particular, it is proved that every hypercyclic operator on a real or complex Banach space has a dense invariant linear manifold with maximal algebraic dimension consisting, apart from zero, of vectors which are hypercyclic.
4
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The algebraic size of the family of injective operators

100%
Bernal-González L.
Open Mathematics
|
2017
|
tom 15
|
nr 1
13-20
EN
In this paper, a criterion for the existence of large linear algebras consisting, except for zero, of one-to-one operators on an infinite dimensional Banach space is provided. As a consequence, it is shown that every separable infinite dimensional Banach space supports a commutative infinitely generated free linear algebra of operators all of whose nonzero members are one-to-one. In certain cases, the assertion holds for nonseparable Banach spaces.
5
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Algebraic genericity of strict-order integrability

100%
Bernal-González L.
Studia Mathematica
|
2010
|
tom 199
|
nr 3
279-293
EN
We provide sharp conditions on a measure μ defined on a measurable space X guaranteeing that the family of functions in the Lebesgue space $L^{p}(μ,X)$ (p ≥ 1) which are not q-integrable for any q > p (or any q < p) contains large subspaces of $L^{p}(μ,X)$ (without zero). This improves recent results due to Aron, García, Muñoz, Palmberg, Pérez, Puglisi and Seoane. It is also shown that many non-q-integrable functions can even be obtained on any nonempty open subset of X, assuming that X is a topological space and μ is a Borel measure on X with appropriate properties.
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