Stably isomorphic dual operator algebras

TL;DR

This paper establishes a characterization of stable isomorphism between unital dual operator algebras through Delta-equivalence and the existence of specific ternary rings of operators, linking algebraic and representation-theoretic properties.

Contribution

It provides a new equivalence criterion for stable isomorphism of dual operator algebras using ternary rings of operators and normal representations.

Findings

Stable isomorphism is equivalent to Delta-equivalence.

Existence of a ternary ring of operators characterizes stable isomorphism.

Normal representations relate the algebras via specific operator equations.

Abstract

We prove that two unital dual operator algebras A, B are stably isomorphic if and only if they are Delta-equivalent, if and only if they have completely isometric normal representations a, b on Hilbert spaces H, K respectively and there exists a ternary ring of operators M \subset B(H,K) such that a(A)=[M* b(B) M]^{-w^*} and b(B)=[M a(A) M*]^{-w^*}.