Lilian Lourenco - Academia.edu (original) (raw)

Uploads

Papers by Lilian Lourenco

Studia Mathematica, 2007

Let A ∞ (B X) be the Banach space of all bounded and continuous functions on the closed unit ball... more Let A ∞ (B X) be the Banach space of all bounded and continuous functions on the closed unit ball B X of a complex Banach space X and holomorphic on the open unit ball, with sup norm, and let A u (B X) be the subspace of A ∞ (B X) of those functions which are uniformly continuous on B X. A subset B ⊂ B X is a boundary for A ∞ (B X) if f = sup x∈B |f (x)| for every f ∈ A ∞ (B X). We prove that for X = d(w, 1) (the Lorentz sequence space) and X = C 1 (H), the trace class operators, there is a minimal closed boundary for A ∞ (B X). On the other hand, for X = S, the Schreier space, and X = K(ℓ p , ℓ q) (1 ≤ p ≤ q < ∞), there is no minimal closed boundary for the corresponding spaces of holomorphic functions.

Journal of Mathematical Analysis and Applications, 2000

Archiv der Mathematik, 1989

Rocky Mountain Journal of Mathematics, 2006

We study τ w-continuous homomorphisms on algebras of holomorphic germs. In this setting we give c... more We study τ w-continuous homomorphisms on algebras of holomorphic germs. In this setting we give conditions for these homomorphisms to be composition operators. We also present equivalent conditions for the above homomorphisms to be Montel or reflexive.

The Quarterly Journal of Mathematics, 2009

Complex Variables and Elliptic Equations, 1988

Abstract. We discuss necessary conditions for a Banach space to satisfy the property that its bou... more Abstract. We discuss necessary conditions for a Banach space to satisfy the property that its bounded sets are bounding in its bidual space. Apart from the classic case of c0, we prove that, among others, the direct sum c0(l n 2) is another example of spaces having such property. A subset B of a complex Banach space X is said to be bounding if every entire function dened on X is bounded on B. Such a set is also a limited set (see below) and, of course, every relatively compact set is bounding. If X is such that every bounding subset is relatively compact, then X is called a Gelfand{ Phillips space and there is some literature devoted to the topic. Gelfand{Phillips spaces are characterized also as those whose sequences converging against entire functions are norm convergent [7]. B. Josefson [12] and T. Schlumprecht [15] found simultaneously and independently examples of complex Banach spaces containing limited non-bounding (hence non-relatively compact) sets. By H(X) we denote the sp...

Proceedings of the American Mathematical Society

We study the class of Banach algebra-valued n-homogeneous polynomials generated by the nth powers... more We study the class of Banach algebra-valued n-homogeneous polynomials generated by the nth powers of linear operators. We compare it with the finite type polynomials. We introduce a topology wEFw_{EF}wEF on E, similar to the weak topology, to clarify the features of these polynomials.

Let E, F and G be Banach spaces. Let V a balanced open subset of F. The reflexive and Montel comp... more Let E, F and G be Banach spaces. Let V a balanced open subset of F. The reflexive and Montel composition operator TΦ(f) := f • Φ acting between the Fréchet spaces of all G-valued holomorphic functions of bounded type on E is studied in terms of Φ, where Φ is a G-valued holomorphic functions of bounded type on V .

Annales- Academiae Scientiarum Fennicae Mathematica

We discuss necessary conditions for a Banach space to satisfy the property that its bounded sets ... more We discuss necessary conditions for a Banach space to satisfy the property that its bounded sets are bounding in its bidual space. Apart from the classic case of c 0 , we prove that, among others, the direct sum c 0 (l n 2) is another example of spaces having such property. A subset B of a complex Banach space X is said to be bounding if every entire function defined on X is bounded on B . Such a set is also a limited set (see below) and, of course, every relatively compact set is bounding. If X is such that every bounding subset is relatively compact, then X is called a Gelfand– Phillips space and there is some literature devoted to the topic. Gelfand–Phillips spaces are characterized also as those whose sequences converging against entire functions are norm convergent [7]. B. Josefson [12] and T. Schlumprecht [15] found simultaneously and independently examples of complex Banach spaces containing limited non-bounding (hence non-relatively compact) sets. By H(X) we denote the space...

Publications of the Research Institute for Mathematical Sciences, 2001

Let E be a complex Banach space and F be a complex Banach algebra. We will be interested in the s... more Let E be a complex Banach space and F be a complex Banach algebra. We will be interested in the subspace IP f (n E, F) of P (n E, F) generated by the collection of functions ϕ n (n ∈ AE, ϕ ∈ L(E, F)) where ϕ n (x) = (ϕ(x)) n for each x ∈ E.

Mathematische Nachrichten, 2002

We study homomorphisms between Fréchet algebras of holomorphic functions of bounded type. In this... more We study homomorphisms between Fréchet algebras of holomorphic functions of bounded type. In this setting we prove that any pointwise bounded homomorphism into the space of entire functions of bounded type is rank one. We characterize, up to the approximation property of the underlying Banach space, the weakly compact composition operators on H b (V), V an absolutely convex open set.

Mathematica Slovaca, 2008

We show that a 2-homogeneous polynomial on the complex Banach space c 0 l 2i) is norm attaining i... more We show that a 2-homogeneous polynomial on the complex Banach space c 0 l 2i) is norm attaining if and only if it is finite (i.e, depends only on finite coordinates). As the consequence, we show that there exists a unique norm-preserving extension for norm-attaining 2-homogeneous polynomials on c 0(l 2i).

Journal of Mathematical Analysis and Applications, 1986

ABSTRACT

Indagationes Mathematicae, 2007

We study the uniqueness of norm-preserving extension of n-homogeneous polynomials on X, where X i... more We study the uniqueness of norm-preserving extension of n-homogeneous polynomials on X, where X is a c0-sum of Hilbert spaces. We show that there exists a unique norm-preserving extension for normattaining 2-homogeneous polynomials on X to X', but this result fails for homogeneous polynomials of degree greater than 2.

Glasgow Mathematical Journal, 2006

Let (e n) be the canonical basis of the predual of the Lorentz sequence space d * (w, 1). We cons... more Let (e n) be the canonical basis of the predual of the Lorentz sequence space d * (w, 1). We consider the restriction operator R associated to the basis (e i) from some Banach space of analytic functions into the complex sequence space and we characterize the ranges of R.

Nonlinear Analysis: Theory, Methods & Applications, 2014

We show that the space of bounded linear operators between spaces of continuous functions on comp... more We show that the space of bounded linear operators between spaces of continuous functions on compact Hausdorff topological spaces has the Bishop-Phelps-Bollobás property. A similar result is also proved for the class of compact operators from the space of continuous functions vanishing at infinity on a locally compact and Hausdorff topological space into a uniformly convex space, and for the class of compact operators from a Banach space into a predual of an L 1-space.