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We show that the set L of complex-valued everywhere surjective functions on C is aJgebrable. Specifically, L contains an infinitely generated algebra every non-zero element of which is everywhere surjective. We also give a technique to construct[...]texto impreso
Aron, Richard M. ; Pérez García, David ; Seoane-Sepúlveda, Juan B. | Polish Acad Sciencies Inst Mathematics | 2006We show that, given a set E subset of T of measure zero, the set of continuous functions whose Fourier series expansion is divergent at any point t is an element of E is dense-algebrable, i.e. there exists an infinite-dimensional, infinitely gen[...]texto impreso
In this paper we prove that given any two disjoint balls in an infinite dimensional complex Banach space, there exists an entire function which is bounded on one and unbounded on the other.texto impreso
We give a sufficient condition for an operator to be chaotic and we use this condition to show that, in the Banach space C-0[0, infinity) the operator (T(lambda,c)f) (t) = lambda f (t + c) (with lambda > 1 and c > 0) is chaotic, with every n i[...]texto impreso
Let E and F be Banach spaces and let Cwu(E) be the Fréchet algebra of real-valued functions on E which are uniformly weakly continuous when restricted to any bounded subset of E. Homomorphisms, and properties of such homomorphisms, between Cwu(E[...]texto impreso
Let U be an open subset of a complex locally convex space E, let F be a closed subspace of E, and let PI:E --> E/F be the canonical quotient mapping. In this paper we study the induced mapping PI*, taking f is-an-element-of H(b)(PI(U))--> f ci[...]texto impreso
In this work we investigate the inverse approximation problems in the Lebesgue and Smirnov spaces with weights satisfying the so-called Muckenhoupt's Ap condition in terms of the -th mean modulus of smoothness, > 0. We obtain a converse theore[...]texto impreso
Let E and F be two real Banach spaces. For n = 0, 1, ...,1, let Cnw ub(E; F) be the space of n-times continuously differentiable functions f: E ! F such that, for each integer j _ n and each x 2 E, both the jth derivative mapping fj : E ! P(jE; [...]texto impreso
We show that no power of any entire function is hypercyclic for Birkhoff's translation operator on H(C). On the other hand, we see that the set of functions whose powers are all hypercyclic for MacLane's differentiation operator is a G(delta)-de[...]texto impreso
Ansemil, José María M. ; Aron, Richard M. ; Ponte, Socorro | European Mathematical Society | 2009-06We prove the impossibility of expressing the space of entire functions on any infinite dimensional complex Banach space with a Schauder basis E as a countable union of spaces of entire functions that are bounded on countable open covers of E.texto impreso
Given a surjective mapping f : E -> F between Banach spaces, we investigate the existence of a subspace G of E, with the same density character as F, such that the restriction of f to G remains surjective. We obtain a positive answer whenever f[...]texto impreso
Let f : E -> F be a surjective mapping between two real or complex Banach spaces, with f having some strong differentiability properties. We investigate when there is a smaller Banach space G subset of E such that the restriction of f to G rema[...]texto impreso
Let E be a complex locally convex space, F a closed subspace, and let ? be the canonical quotient mapping from E onto E/F. Let H(U) [resp. H(K)] be the set of holomorphic functions on the open set U of E [resp. the set of germs of holomorphic fu[...]texto impreso
Aron, Richard M. ; Conejero, Jose A. ; Peris, Alfredo ; Seoane-Sepúlveda, Juan B. | American Mathematical Society | 2007We examine the question of whether there are algebras of functions having special properties. The types of functions studied will be everywhere surjective functions, hypercyclic entire functions, and continuous functions that attain their maximu[...]texto impreso
Aron, Richard M. ; Conejero, Jose A. ; Peris, Alfredo ; Seoane-Sepúlveda, Juan B. | Société mathématique de Belgique | 2010We show that there exists an uncountably generated algebra every non-zero element of which is an everywhere surjective function on C, that is, a function f : C -> C such that, for every non void open set U subset of C, f(U) = C.
