Nonlinear Jordan Derivations of Triangular Algebras

TL;DR

This paper proves that nonlinear Jordan derivations on triangular and nest algebras are additive derivations and inner, respectively, revealing their structural properties in algebraic and operator algebra contexts.

Contribution

It establishes that nonlinear Jordan derivations on triangular algebras are additive derivations and that on nest algebras over infinite-dimensional Hilbert spaces they are inner, advancing understanding of derivation structures.

Findings

Nonlinear Jordan derivations on triangular algebras are additive derivations.

Nonlinear Jordan derivations on nest algebras over infinite-dimensional Hilbert spaces are inner.

Provides new insights into the structure of derivations in algebra and operator algebra settings.

Abstract

In this paper we prove that any nonlinear Jordan derivation on triangular algebras is an additive derivation. As a byproduct, we obtain that any nonlinear Jordan derivation on nest algebras over infinite dimensional Hilbert spaces is inner.