Some analysis on amalgamated free products of von Neumann algebras in non-tracial setting

Several techniques together with some partial answers are given to the questions of factoriality, type classification and fullness for amalgamated free product von Neumann algebras.Comment: 3rd version; no essential change; typos correcte

Discrete cores of type III free product factors

We give a general description of the discrete decompositions of type III factors arising as central summands of free product von Neumann algebras based on our previous works. This enables us to give several precise structural results on type III free product factors.Comment: Expanded versio

On type III_1 factors arising as free products

Type III_1 factors arising as (direct summands of) von Neumann algebraic free products are investigated. In particular we compute Connes' Sd- and tau- invariants for those type III_1 factors without any extra assumption.Comment: 10 pages, "almost" final version; to appear in Math. Res. Let

Free product actions and their applications

A review of our recent works on free product actions, partly in collaborations with Dimitri Shlyakhtenko and with Fumio Hiai, is given. We also work out type III theoretic subfactor analysis on the subfactors constructed in our previous works. This part can be read as supplementary appendix to the works.Comment: To appear in "Non-Commutativity, Infinite-Dimensionality and Probability at the Crossroads," World Scientifi

On the predual of non-commutative H∞H^\infty

The unique predual $M_\star/A_\perp$ of a non-commutative $H^\infty$-algebra $A = H^\infty(M,\tau)$ is investigated. In particular, we will prove the liftability property of weakly relatively compact subsets in $M_\star/A_\perp$ to $M_\star$.Comment: 10 pages, Final version, to appear in BLM

Orbital free entropy, revisited

We give another definition of orbital free entropy introduced by Hiai, Miyamoto and us, which does not need the hyperfiniteness assumption for each given random multi-variable. The present definition is somehow related to one of its several recent `generalizations' due to Biane and Dabrowski, but completely agrees with the original definition and much closer to the original approach.Comment: 19 pages; final versio