Richard M. Aron
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Richard M. Aron has a total of 45 co-authors. Here are the top co-authors by number of shared publications:
- Manuel Maestre
Departamento de Análisis Matemático, Universidad de Valencia, Burjasot, Spain
12 shared publications - Domingo García
Departamento de Análisis Matemático, Universidad de Valencia, Burjasot, Spain
7 shared publications - Paul M. Gauthier
Univ Montreal, Dept Math & Stat, Montreal, PQ H3C 3J7, Canada
3 shared publications - Vassili Nestoridis
Department of Mathematics, National and Kapodistrian University of Athens, Athens, Greece
3 shared publications - Frédéric Bayart
Clermont Université, Université Blaise Pascal
2 shared publications - Han Ju Lee
Department of Mathematics Education, Dongguk University - Seoul, Seoul, Republic of Korea
2 shared publications
Latest Publications
- 24 September 2026
- Published by Taylor & Francis in Integral Transforms and Special Functions
- p. 1-11
A note on differentials of holomorphic functions
1. In [1], the authors study the space HL0(BX) of holomorphic Lipschitz functions defined on BX, the open unit ball of the complex Banach space X that take the value 0 at 0, endowed with the Lipsch...
- 24 September 2026
- Published by Taylor & Francis in Integral Transforms and Special Functions
- p. 1-11
A note on differentials of holomorphic functions
1. In [1], the authors study the space HL0(BX) of holomorphic Lipschitz functions defined on BX, the open unit ball of the complex Banach space X that take the value 0 at 0, endowed with the Lipsch...
- Open Access
- 1 May 2025
- Published by Springer Nature in Journal of Mathematical Sciences
- Vol. 290 (3) , 329-334
SOME COMMENTS ABOUT LINEABILITY AND NON-LINEABILITY
We give a brief account of some early and some recent results in the area now known as “lineability” and “spaceability.” Several examples, results, and open questions shall be presented. This article is an expanded version of a lecture given by the first author at a satellite conference of the 9ECM during June 2024, “From Classical to Modern Analysis: In memory of Professor José Carlos Petronilho.”
- 1 May 2025
- Published by Springer Nature in Journal of Mathematical Sciences
- Vol. 290 (3) , 329-334
Open AccessSOME COMMENTS ABOUT LINEABILITY AND NON-LINEABILITY
We give a brief account of some early and some recent results in the area now known as “lineability” and “spaceability.” Several examples, results, and open questions shall be presented. This article is an expanded version of a lecture given by the first author at a satellite conference of the 9ECM during June 2024, “From Classical to Modern Analysis: In memory of Professor José Carlos Petronilho.”
- Open Access
- 23 January 2024
- Published by Springer Nature in Results in Mathematics
- Vol. 79 (2) , 1-20
Norm Attaining Elements of the Ball Algebra $H^\infty (B_N)$Let $$B_N$$ be the Euclidean ball of $${\mathbb {C}}^N$$ . The space $$H^\infty (B_N)$$ of bounded holomorphic functions on $$B_N$$ is known to have a predual, denoted by $$G^\infty (B_N)$$ . We study the functions in $$H^\infty (B_N)$$ that attain their norm as elements of the dual of $$G^\infty (B_N)$$ . We also examine similar questions for the polydisc algebra $$H^\infty ({\mathbb {D}}^N)$$ and for the space of Dirichlet series $$ {\mathcal {D}}^\infty ({\mathbb {C}}_+).$$- 23 January 2024
- Published by Springer Nature in Results in Mathematics
- Vol. 79 (2) , 1-20
Open AccessNorm Attaining Elements of the Ball Algebra $H^\infty (B_N)$Let $$B_N$$ be the Euclidean ball of $${\mathbb {C}}^N$$ . The space $$H^\infty (B_N)$$ of bounded holomorphic functions on $$B_N$$ is known to have a predual, denoted by $$G^\infty (B_N)$$ . We study the functions in $$H^\infty (B_N)$$ that attain their norm as elements of the dual of $$G^\infty (B_N)$$ . We also examine similar questions for the polydisc algebra $$H^\infty ({\mathbb {D}}^N)$$ and for the space of Dirichlet series $$ {\mathcal {D}}^\infty ({\mathbb {C}}_+).$$ - Open Access
Linearization of holomorphic Lipschitz functions
Let $X$ and $Y$ be complex Banach spaces with $B_X$ denoting the open unit ball of $X.$ This paper studies various aspects of the {\em holomorphic Lipschitz space} $\mathcal HL_0(B_X,Y)$, endowed with the Lipschitz norm. This space is the intersection of the spaces, $\operatorname{Lip}_0(B_X,Y)$ of Lipschitz mappings and $\mathcal H^\infty(B_X,Y)$ of bounded holomorphic mappings, from $B_X$ to $Y$. Thanks to the Dixmier-Ng theorem, $\mathcal HL_0(B_X, \mathbb C)$ is indeed a dual space, whose predual $\mathcal G_0(B_X)$ shares linearization properties with both the Lipschitz-free space and Dineen-Mujica predual of $\mathcal H^\infty(B_X)$. We explore the similarities and differences between these spaces, and combine techniques to study the properties of the space of holomorphic Lipschitz functions. In particular, we get that $\mathcal G_0(B_X)$ contains a 1-complemented subspace isometric to $X$ and that $\mathcal G_0(X)$ has the (metric) approximation property whenever $X$ has it. We also analyze when $\mathcal G_0(B_X)$ is a subspace of $\mathcal G_0(B_Y)$, and we obtain an analogous to Godefroy's characterization of functionals with a unique norm preserving extension to the holomorphic Lipschitz context.Open AccessLinearization of holomorphic Lipschitz functions
Let $X$ and $Y$ be complex Banach spaces with $B_X$ denoting the open unit ball of $X.$ This paper studies various aspects of the {\em holomorphic Lipschitz space} $\mathcal HL_0(B_X,Y)$, endowed with the Lipschitz norm. This space is the intersection of the spaces, $\operatorname{Lip}_0(B_X,Y)$ of Lipschitz mappings and $\mathcal H^\infty(B_X,Y)$ of bounded holomorphic mappings, from $B_X$ to $Y$. Thanks to the Dixmier-Ng theorem, $\mathcal HL_0(B_X, \mathbb C)$ is indeed a dual space, whose predual $\mathcal G_0(B_X)$ shares linearization properties with both the Lipschitz-free space and Dineen-Mujica predual of $\mathcal H^\infty(B_X)$. We explore the similarities and differences between these spaces, and combine techniques to study the properties of the space of holomorphic Lipschitz functions. In particular, we get that $\mathcal G_0(B_X)$ contains a 1-complemented subspace isometric to $X$ and that $\mathcal G_0(X)$ has the (metric) approximation property whenever $X$ has it. We also analyze when $\mathcal G_0(B_X)$ is a subspace of $\mathcal G_0(B_Y)$, and we obtain an analogous to Godefroy's characterization of functionals with a unique norm preserving extension to the holomorphic Lipschitz context. - Open Access
- 13 October 2022
- Published by Springer Nature in Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas
- Vol. 117 (1) , 1-10
Farkas’ Lemma in the bilinear setting and evaluation functionals
We prove the following Farkas’ Lemma for simultaneously diagonalizable bilinear forms: If $$A_1,\ldots ,A_k$$ , and $$B:\mathbb {R}^n \times \mathbb {R}^n \rightarrow \mathbb {R}$$ are bilinear forms, then one—and only one—of the following holds: $$B=a_1 A_1 + \cdots + a_k A_k,$$ with non-negative $$a_i\text {'s}$$ , there exists (x, y) for which $$A_1(x,y) \ge 0 , \ldots , A_k(x,y) \ge 0$$ and $$B(x,y) < 0$$ . We study evaluation maps over the space of bilinear forms and consequently construct examples in which Farkas’ Lemma fails in the bilinear setting.- 13 October 2022
- Published by Springer Nature in Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas
- Vol. 117 (1) , 1-10
Open AccessFarkas’ Lemma in the bilinear setting and evaluation functionals
We prove the following Farkas’ Lemma for simultaneously diagonalizable bilinear forms: If $$A_1,\ldots ,A_k$$ , and $$B:\mathbb {R}^n \times \mathbb {R}^n \rightarrow \mathbb {R}$$ are bilinear forms, then one—and only one—of the following holds: $$B=a_1 A_1 + \cdots + a_k A_k,$$ with non-negative $$a_i\text {'s}$$ , there exists (x, y) for which $$A_1(x,y) \ge 0 , \ldots , A_k(x,y) \ge 0$$ and $$B(x,y) < 0$$ . We study evaluation maps over the space of bilinear forms and consequently construct examples in which Farkas’ Lemma fails in the bilinear setting. - 23 September 2019
- Published by Springer Nature in Revista Matemática Complutense
- Vol. 33 (2) , 415-436
Gleason parts for algebras of holomorphic functions in infinite dimensions
- 23 September 2019
- Published by Springer Nature in Revista Matemática Complutense
- Vol. 33 (2) , 415-436
Gleason parts for algebras of holomorphic functions in infinite dimensions
- 7 August 2019
- Published by American Mathematical Society (AMS) in Proceedings of the American Mathematical Society
- Vol. 148 (2) , 741-750
Reflexivity and nonweakly null maximizing sequences
We introduce and explore a new property related to reflexivity that plays an important role in the characterization of norm attaining operators. We also present an application to the theory of compact perturbations of linear operators and characterize norm attaining scalar-valued continuous 2 2 -homogeneous polynomials on ℓ 2 \ell _{2} .
- 7 August 2019
- Published by American Mathematical Society (AMS) in Proceedings of the American Mathematical Society
- Vol. 148 (2) , 741-750
Reflexivity and nonweakly null maximizing sequences
We introduce and explore a new property related to reflexivity that plays an important role in the characterization of norm attaining operators. We also present an application to the theory of compact perturbations of linear operators and characterize norm attaining scalar-valued continuous 2 2 -homogeneous polynomials on ℓ 2 \ell _{2} .
- 1 January 2019
- Published by Institute of Mathematics, Polish Academy of Sciences in Annales Polonici Mathematici
- Vol. 123 (1) , 31-41
Extendability and domains of holomorphy in infinite-dimensional spaces
- 1 January 2019
- Published by Institute of Mathematics, Polish Academy of Sciences in Annales Polonici Mathematici
- Vol. 123 (1) , 31-41
Extendability and domains of holomorphy in infinite-dimensional spaces
- Open Access
Smooth surjections and surjective restrictions
Given a surjective mapping $f : E \to F$ 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 $f$ is continuous and uniformly open. In the smooth case, we deduce a positive answer when $f$ is a $C^1$-smooth surjection whose set of critical values is countable. Finally we show that, when $f$ takes values in the Euclidean space $\mathbb R^n$, in order to obtain this result it is not sufficient to assume that the set of critical values of $f$ has zero-measure.Open AccessSmooth surjections and surjective restrictions
Given a surjective mapping $f : E \to F$ 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 $f$ is continuous and uniformly open. In the smooth case, we deduce a positive answer when $f$ is a $C^1$-smooth surjection whose set of critical values is countable. Finally we show that, when $f$ takes values in the Euclidean space $\mathbb R^n$, in order to obtain this result it is not sufficient to assume that the set of critical values of $f$ has zero-measure. - 1 May 2018
- Published by Elsevier in Linear Algebra and its Applications
- Vol. 544, 186-205
On the size of special families of linear operators
- 1 May 2018
- Published by Elsevier in Linear Algebra and its Applications
- Vol. 544, 186-205
On the size of special families of linear operators