Searcharxiv⌕ Search

arXiv subjects

A. M. Peralta

Publications and source records attributed to A. M. Peralta.

3 recordsLinked to original sources
arXiv2022

Similarities and differences between real and complex Banach spaces: an overview and recent developments

There are numerous cases of discrepancies between results obtained in the setting of real Banach spaces and those obtained in the complex context. This article is a modern exposition of the subtle differences between key results and theories for complex and real Banach spaces and the corresponding linear operators between them. We deeply discuss some aspects of the complexification of real Banach spaces and give several examples showing how drastically different can be the behavior of real Banach spaces versus their complex counterparts.

math.FA↗
arXiv2016

Inner derivations and weak-2-local derivations on the C$^*$-algebra $C_0(L,A)$

Let $L$ be a locally compact Hausdorff space. Suppose $A$ is a C$^*$-algebra with the property that every weak-2-local derivation on $A$ is a {\rm(}linear{\rm)} derivation. We prove that every weak-2-local derivation on $C_0(L,A)$ is a {\rm(}linear{\rm)} derivation. Among the consequences we establish that if $B$ is an atomic von Neumann algebra or on a compact C$^*$-algebra, then every weak-2-local derivation on $C_0(L,B)$ is a linear derivation. We further show that, for a general von Neumann algebra $M$, every 2-local derivation on $C_0(L,M)$ is a linear derivation. We also prove several results representing derivations on $C_0(L,B(H))$ and on $C_0(L,K(H))$ as inner derivations determined by multipliers.

math.OA↗
arXiv2016

Weak-local triple derivations on C*-algebras and JB*-triples

We prove that every weak-local triple derivation on a JB$^*$-triple $E$ (i.e. a linear map $T: E\to E$ such that for each $ϕ\in E^*$ and each $a\in E$, there exists a triple derivation $δ_{a,ϕ} : E\to E$, depending on $ϕ$ and $a$, such that $ϕT(a) = ϕδ_{a,ϕ} (a)$) is a (continuous) triple derivation.

math.OA↗