Note on bi-exactness for creation operators on Fock spaces

Abstract

In this note, we introduce and study a notion of bi-exactness for creation operators acting on full, symmetric and anti-symmetric Fock spaces. This is a generalization of our previous work, in which we studied the case of anti-symmetric Fock spaces. As a result, we obtain new examples of solid actions as well as new proofs for some known solid actions. We also study free wreath product groups in the same context.

arXiv comment37 pages

References in corpus (3)

• Structure of $\mathrm{I}{\mathrm{I}}_1$ factors arising from free Bogoljubov actions of arbitrary groups
• Strongly solid $\mathrm{I}{\mathrm{I}}_1$ factors with an exotic MASA
• Boundary and rigidity of nonsingular Bernoulli actions