# Jordan operator algebras: Basic theory

## TL;DR

This paper introduces a comprehensive and accessible theory of Jordan operator algebras, revealing their close similarities to associative operator algebras and expanding understanding of their structure.

## Contribution

It initiates the theory of nonselfadjoint Jordan operator algebras, demonstrating their deep connection to associative operator algebras.

## Key findings

- Existence of a large, manageable theory of nonselfadjoint Jordan operator algebras
- Jordan operator algebras are more similar to associative operator algebras than previously thought
- Foundation laid for further research in the structure and applications of Jordan operator algebras

## Abstract

Jordan operator algebras are norm-closed spaces of operators on a Hilbert space which are closed under the Jordan product. The discovery of the present paper is that there exists a huge and tractable theory of possibly nonselfadjoint Jordan operator algebras; they are far more similar to associative operator algebras than was suspected. We initiate the theory of such algebras.