# Morita embeddings for dual operator algebras and dual operator spaces

## TL;DR

This paper introduces a new Morita-type relation for dual operator algebras and spaces, exploring its properties, transitivity, and implications for stable isomorphism, advancing the understanding of dual operator structures.

## Contribution

It defines a novel relation < for dual operator algebras and spaces, analyzing its properties and potential to characterize stable isomorphism between these structures.

## Key findings

- < is transitive for dual operator algebras
- Investigates conditions under which A < B and B < A imply stable isomorphism
- Proposes an analogous < relation for dual operator spaces

## Abstract

We define a relation < for dual operator algebras. We say that B < A if there exists a projection p in A such that B and pAp are Morita equivalent in our sense. We show that < is transitive, and we investigate the following question: If A < B and B < A, then is it true that A and B are stably isomorphic? We propose an analogous relation < for dual operator spaces, and we present some properties of < in this case.