Morita equivalence of nest algebras

TL;DR

This paper establishes a deep connection between the isomorphism of nests and Morita equivalence of their associated nest algebras and compact operator subalgebras, providing a characterization of nest isomorphisms that induce stable isomorphisms.

Contribution

It proves that nest isomorphism is equivalent to weak-* Morita equivalence of nest algebras and strong Morita equivalence of their compact operator subalgebras, and characterizes nest isomorphisms inducing stable isomorphisms.

Findings

Nest isomorphism iff weak-* Morita equivalence of nest algebras

Strong Morita equivalence of compact operator subalgebras

Characterization of nest isomorphisms implementing stable isomorphism

Abstract

Let N_1 (resp.N_2) be a nest A (resp. B) be the corresponding nest algebra, A_0 (resp. B_0) be the subalgebra of compact operators. We prove that the nests N_1, N_2 are isomorphic if and only if the algebras A, B are weakly-* Morita equivalent if and only if the algebras A_0, B_0 are strongly Morita equivalent. We characterize the nest isomorphisms which implement stable isomorphism between the corresponding nest algebras.