A. Villena

activity

20122024

most citedZero Lie product determined Banach algebras

8 citations · 16 across the 13 of their papers we have counts for

collaborators

13 papers

math.FA2024

Isometric Jordan isomorphisms of group algebras

J. Alaminos, J. Extremera, C. Godoy +1

Let $G$ and $H$ be locally compact groups. We will show that each contractive Jordan isomorphism $Φ : L^{1} (G) \to L^{1} (H)$ is either an isometric isomorphism or an isometric anti-…

math.FA2023

Lie--Trotter formulae in Jordan--Banach algebras with applications to the study of spectral-valued multiplicative functionals

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

We establish some Lie--Trotter formulae for unital complex Jordan--Banach algebras, showing that for each couple of elements $a, b$ in a unital complex Jordan--Banach algebra $\math…

math.FA2022★ 2 cited

Derivations and homomorphisms in commutator-simple algebras

J. Alaminos, M. Brešar, J. Extremera +2

We call an algebra $A$ commutator-simple if $[A, A]$ does not contain nonzero ideals of $A$ . After providing several examples, we show that in these algebras derivations are determi…

math.FA2021

Maps preserving two-sided zero products on Banach algebras

M. Brešar, M. L. C. Godoy, A. R. Villena

Let $A$ and $B$ be Banach algebras with bounded approximate identities and let $Φ : A \to B$ be a surjective continuous linear map which preserves two-sided zero products (i.e., $Φ(a)…

math.FA2021

Strongly zero product determined Banach algebras

J. Alaminos, J. Extremera, M. L. C. Godoy +1

$C^{*}$ -algebras, group algebras, and the algebra $A (X)$ of approximable operators on a Banach space $X$ having the bounded approximation property are known to be zero prod…

math.OA2020

Hyperreflexivity of the space of module homomorphisms between non-commutative $L^{p}$ -spaces

J. Alaminos, J. Extremera, M. L. C. Godoy +1

Let $M$ be a von Neumann algebra, and let $0 < p, q \leq \infty$ . Then the space $\Hom_\mathcal{M}(L^p(\mathcal{M}),L^q(\mathcal{M}))$ of all right $M$ -module homomor…

math.FA2019★ 4 cited

Zero Jordan product determined Banach algebras

J. Alaminos, M. Brešar, J. Extremera +1

A Banach algebra $A$ is said to be a zero Jordan product determined Banach algebra if every continuous bilinear map $φ : A \times A \to X$ , where $X$ is an arbitrary Banach space…

math.FA2018

Orthogonally additive polynomials on convolution algebras associated with a compact group

J. Alaminos, J. Extremera, M. L. C. Godoy +1

Let $G$ be a compact group, let $X$ be a Banach space, and let $P : L^{1} (G) \to X$ be an orthogonally additive, continuous $n$ -homogeneous polynomial. Then we show that there exi…

math.FA2018★ 2 cited

Orthogonally additive polynomials on the algebras of approximable operators

J. Alaminos, M. L. C. Godoy, A. R. Villena

Let $X$ and $Y$ be Banach spaces, let $A (X)$ stands for the algebra of approximable operators on $X$ , and let $P : A (X) \to Y$ be an orthogonally additive, co…

math.FA2017

Zero Lie product determined Banach algebras, II

J. Alaminos, M. Bresar, J. Extremera +1

A Banach algebra $A$ is said to be zero Lie product determined if every continuous bilinear functional $φ : A \times A \to C$ satisfying $φ (a, b) = 0$ whenever $ab = ba$ is o…

math.FA2016★ 8 cited

Zero Lie product determined Banach algebras

J. Alaminos, M. Brešar, J. Extremera +1

A Banach algebra $A$ is said to be zero Lie product determined if every continuous bilinear functional $φ : A \times A \to C$ with the property that $φ (a, b) = 0$ whenever…

math.OA2013

Derivations preserving quasinilpotent elements

J. Alaminos, M. Brešar, J. Extremera +2

We consider a Banach algebra $A$ with the property that, roughly speaking, sufficiently many irreducible representations of $A$ on nontrivial Banach spaces do not vanish on all squ…

math.RA2012

Maps preserving zeros of a polynomial

J. Alaminos, M. Brešar, Š. Špenko +1

Let $\A$ be an algebra and let $f (x_{1}, ..., x_{d})$ be a multilinear polynomial in noncommuting indeterminates $x_{i}$ . We consider the problem of describing linear maps $ϕ:\A\to \A$ tha…

Isometric Jordan isomorphisms of group algebras

Lie--Trotter formulae in Jordan--Banach algebras with applications to the study of spectral-valued multiplicative functionals

Derivations and homomorphisms in commutator-simple algebras

Maps preserving two-sided zero products on Banach algebras

Strongly zero product determined Banach algebras

Hyperreflexivity of the space of module homomorphisms between non-commutative Lp-spaces

Zero Jordan product determined Banach algebras

Orthogonally additive polynomials on convolution algebras associated with a compact group

Orthogonally additive polynomials on the algebras of approximable operators

Zero Lie product determined Banach algebras, II

Zero Lie product determined Banach algebras

Derivations preserving quasinilpotent elements

Maps preserving zeros of a polynomial

Hyperreflexivity of the space of module homomorphisms between non-commutative $L^{p}$ -spaces