2-Local derivations on algebras of matrix-valued functions on a compact

TL;DR

This paper proves that all 2-local derivations on algebras of infinite dimensional matrix-valued functions over a compact are actual derivations, extending the method to various algebra types.

Contribution

It establishes that 2-local derivations on these algebras are derivations and introduces a versatile method applicable to multiple algebra structures.

Findings

Every 2-local derivation is a derivation on these algebras.

The method applies to associative, Jordan, and Lie algebras of matrix-valued functions.

The approach simplifies understanding derivations in infinite-dimensional contexts.

Abstract

In the present paper 2-local derivations on various algebras of infinite dimensional matrix-valued functions on a compact are considered. It is proved that every 2-local derivation on such algebra is a derivation. Also we explain that the method developed in the given paper can be applied to associative, Jordan and Lie algebras of infinite dimensional matrix-valued functions on a compact.