Antonio M. Peralta

activity

20242026

collaborators

16 papers

math.OA2026

Numerical index one characterises commutative JB*-triples

Lei Li, Siyu Liu, Antonio M. Peralta

We establish that a JB $^{*}$ -triple $E$ is commutative if and only if its numerical index $n (E)$ is one. As a consequence, $n (E) = 1$ implies $n (E^{*}) = n (E^{**}) = 1$ . This settles a…

math.FA2026

A Le Page--Kaplansky theorem characterizing commutative JB*-triples

Lei Li, Siyu Liu, Antonio M. Peralta

We prove that a Le Page-type inequality is also valid for metrically characterizing those JB $^{*}$ -triples that are commutative. More precisely, we establish that the following state…

math.OA2026

Quadratic & additive mappings on operator commuting elements in JBW*-algebras

Gerardo M. Escolano, Jan Hamhalter, Antonio M. Peralta +1

Let $A$ and $B$ be JBW $^{*}$ -algebras whose sets of unitaries are denoted by $U (A)$ and $U (B)$ , respectively. We show…

math.OA2026

A metric characterization of projections among positive norm-One elements in unital C $^{*}$ -algebras

Antonio M. Peralta, Pedro Saavedra

We characterize projections among positive norm-one elements in unital C $^{*}$ -algebras in pure geometric terms determined by the norm of the underlying Banach space. Concretely, let…

math.OA2025

New insights into linear maps which are anti-derivable at zero

Jiankui Li, Antonio M. Peralta, Shanshan Su

Let $A$ be a Banach algebra admitting a bounded approximate unit and satisfying property $B$ . Suppose $T : A \to X$ is a continuous linear map, where $X$ is an esse…

math.OA2025

Uniqueness of Hahn--Banach extensions and inner ideals in real C $^{}$ -algebras and real JB $^{}$ -triples

Lei Li, Antonio M. Peralta, Shanshan Su +1

We show that every closed (resp., weak $^{*}$ -closed) inner ideal $I$ of a real JB $^{*}$ -triple (resp. a real JBW $^{*}$ -triple) $E$ is Hahn--Banach smooth (resp., weak $^{*}$ -Hahn--Banach sm…

math.OA2025

The Mackey-Gleason-Bunce-Wright problem for vector-valued measures on projections in a JBW $^{*}$ -algebra

Gerardo M. Escolano, Antonio M. Peralta, Armando R. Villena

Let $P (J)$ denote the lattice of projections of a JBW $^{*}$ -algebra $J$ , and let $X$ be a Banach space. A bounded finitely additive $X$ -valued measur…

math.OA2025

Identifying JBW $^{*}$ -algebras through their spheres of positive elements

Antonio M. Peralta, Pedro Saavedra

Let $A$ and $B$ be JBW $^{*}$ -algebras with projection lattices $P (A)$ and $P (B)$ , and let $Θ: \mathcal{P} (\mathfrak…

math.FA2025

An algebraic characterization of linearity for additive maps preserving orthogonality

Lei Li, Siyu Liu, Antonio M. Peralta

We study when an additive mapping preserving orthogonality between two complex inner product spaces is automatically complex-linear or conjugate-linear. Concretely, let $H$ and $K$ …

math.OA2024

Characterization of minimal tripotents via annihilators and its application to the study of additive preservers of truncations

Lei Li, Siyu Liu, Antonio M. Peralta

The contributions in this note begin with a new characterization of (positive) scalar multiples of minimal tripotents in a general JB $^{*}$ -triple $E$ , proving that a non-zero elemen…

math.FA2024

Additive mappings preserving orthogonality between complex inner product spaces

Lei Li, Siyu Liu, Antonio M. Peralta

Let $H$ and $K$ be two complex inner product spaces with dim $(X) \geq 2$ . We prove that for each non-zero additive mapping $A : H \to K$ with dense image the following statements are…

math.OA2024

Preservers of Operator Commutativity

Gerardo M. Escolano, Antonio M. Peralta, Armando R. Villena

Let $M$ and $J$ be JBW $^{*}$ -algebras admitting no central summands of type $I_{1}$ and $I_{2},$ and let $Φ : M \to J$ be a linear bije…

math.OA2024

Maps preserving the truncation of triple products on Cartan factors

Jorge J. Garcés, Lei Li, Antonio M. Peralta +1

Let ${C_{i}}_{i \in Γ_{1}},$ and ${D_{j}}_{j \in Γ_{2}},$ be two families of Cartan factors such that all of them have dimension at least $2$ , and consider the atomic JBW $^{*}$ -triples $A=…

math.OA2024

M-ideals in real operator algebras

David P. Blecher, Matthew Neal, Antonio M. Peralta +1

In a recent paper we showed that a subspace of a real JBW*-triple is an M-summand if and only if it is a weak*-closed triple ideal. As a consequence, M-ideals of real JB*-triples,…

math.OA2024

On the equivalence of all notions of generalized derivations whose domain is a C $^{*}$ -algebra

Amin Hosseini, Antonio M. Peralta, Shanshan Su

Let $M$ be a Banach bimodule over an associative Banach algebra $A$ , and let $F : A \to M$ be a linear mapping. Three main uses of the term \e…

math.OA2024

$M$ -ideals, yet again: the case of real JB $^{*}$ -triples

David P. Blecher, Matthew Neal, Antonio M. Peralta +1

We prove that a subspace of a real JBW $^{*}$ -triple is an $M$ -summand if and only if it is a weak $^{*}$ -closed triple ideal. As a consequence, $M$ -ideals of real JB $^{*}$ -triples corresp…

Numerical index one characterises commutative JB*-triples

A Le Page--Kaplansky theorem characterizing commutative JB*-triples

Quadratic & additive mappings on operator commuting elements in JBW*-algebras

A metric characterization of projections among positive norm-One elements in unital C∗-algebras

New insights into linear maps which are anti-derivable at zero

Uniqueness of Hahn--Banach extensions and inner ideals in real C∗-algebras and real JB∗-triples

The Mackey-Gleason-Bunce-Wright problem for vector-valued measures on projections in a JBW∗-algebra

Identifying JBW∗-algebras through their spheres of positive elements

An algebraic characterization of linearity for additive maps preserving orthogonality

Characterization of minimal tripotents via annihilators and its application to the study of additive preservers of truncations

Additive mappings preserving orthogonality between complex inner product spaces

Preservers of Operator Commutativity

Maps preserving the truncation of triple products on Cartan factors

M-ideals in real operator algebras

On the equivalence of all notions of generalized derivations whose domain is a C∗-algebra

M-ideals, yet again: the case of real JB∗-triples

A metric characterization of projections among positive norm-One elements in unital C $^{*}$ -algebras

Uniqueness of Hahn--Banach extensions and inner ideals in real C $^{}$ -algebras and real JB $^{}$ -triples

The Mackey-Gleason-Bunce-Wright problem for vector-valued measures on projections in a JBW $^{*}$ -algebra

Identifying JBW $^{*}$ -algebras through their spheres of positive elements

On the equivalence of all notions of generalized derivations whose domain is a C $^{*}$ -algebra

$M$ -ideals, yet again: the case of real JB $^{*}$ -triples