Jorge J. Garcés

collaborators

7 papers

math.RA2024

Invertibility preservers of finitary incidence algebras

Jorge J. Garcés, Mykola Khrypchenko

Let $X$ be an arbitrary poset and $K$ an arbitrary field. We describe linear unital invertibility preservers of the finitary incidence algebra $F I (X, K)$ in terms of certain maps of…

math.OA2024★ 23 cited

Automatic continuity of biorthogonality preservers between compact C $^{*}$ -algebras and von Neumann algebras

Mar\' ia Burgos, Jorge J. Garcés, Antonio M. Peralta

We prove that every biorthogonality preserving linear surjection between two dual or compact C $^{*}$ -algebras or between two von Neumann algebras is automatically continuous.

math.OA2024★ 7 cited

Generalised triple homomorphisms and Derivations

Jorge J. Garcés, Antonio M. Peralta

We introduce generalised triple homomorphism between Jordan Banach triple systems as a concept which extends the notion of generalised homomorphism between Banach algebras given by…

math.OA2024★ 5 cited

A Kaplansky Theorem for JB*-triples

Francisco J. Fernández-Polo, Jorge J. Garcés, Antonio M. Peralta

Let $T : E \to F$ be a non-necessarily continuous triple homomorphism from a (complex) JB $^{*}$ -triple (respectively, a (real) J $^{*}$ B-triple) to a normed Jordan triple. The foll…

math.OA2024★ 14 cited

Automatic continuity of biorthogonality preservers between weakly compact JB $^{}$ -triples and atomic JBW $^{}$ -triples

María Burgos, Jorge J. Garcés, Antonio M. Peralta

We prove that every biorthogonality preserving linear surjection from a weakly compact JB $^{*}$ triple containing no infinite dimensional rank-one summands onto another JB $^{*}$ -triple…

math.OA2024★ 23 cited

Complete orthogonality preservers between C $^{*}$ -algebras

Jorge J. Garcés

We introduce $n$ -orthogonality (and completely orthogonality) preserving operators between C $^{*}$ -algebras. Our main theorem states that every completely orthogonality preserving bo…