Yusuke Isono
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View article: Haagerup and Størmer's conjecture for pointwise inner automorphisms
Haagerup and Størmer's conjecture for pointwise inner automorphisms Open
In 1988, Haagerup and Størmer conjectured that any pointwise inner automorphism of a type $\rm III_1$ factor is a composition of an inner and a modular automorphism. We study this conjecture and prove that any type $\rm III_1$ factor with …
View article: Pointwise inner automorphisms of almost periodic factors
Pointwise inner automorphisms of almost periodic factors Open
We prove that a large class of nonamenable almost periodic type ${\rm III_1}$ factors $M$, including all McDuff factors that tensorially absorb $R_\infty$ and all free Araki-Woods factors, satisfy Haagerup-Stormer's conjecture (1988): any …
View article: Note on bi-exactness for creation operators on Fock spaces
Note on bi-exactness for creation operators on Fock spaces Open
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 Fo…
View article: Unitary conjugacy for type III subfactors and W$^*$-superrigidity
Unitary conjugacy for type III subfactors and W$^*$-superrigidity Open
Let A,B\subset M be inclusions of \sigma -finite von Neumann algebras such that A and B are images of faithful normal conditional expectations. In this article, we investigate Popa's intertwining condition A\preceq_MB using modular actions…
View article: Note on bi-exactness for creation operators on Fock spaces
Note on bi-exactness for creation operators on Fock spaces Open
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 Fo…
View article: Connes' bicentralizer problem for q‐deformed Araki–Woods algebras
Connes' bicentralizer problem for q‐deformed Araki–Woods algebras Open
Let $(H_{\\mathbf{R}}, U_t)$ be any strongly continuous orthogonal\nrepresentation of $\\mathbf{R}$ on a real (separable) Hilbert space\n$H_{\\mathbf{R}}$. For any $q\\in (-1,1)$, we denote by\n$\\Gamma_q(H_{\\mathbf{R}},U_t)^{\\prime\\pri…
View article: Ergodic theory of affine isometric actions on Hilbert spaces
Ergodic theory of affine isometric actions on Hilbert spaces Open
The classical Gaussian functor associates to every orthogonal representation of a locally compact group $G$ a probability measure preserving action of $G$ called a Gaussian action. In this paper, we generalize this construction by associat…
View article: $L_2$-cohomology, derivations and quantum Markov semi-groups on $q$-Gaussian algebras
$L_2$-cohomology, derivations and quantum Markov semi-groups on $q$-Gaussian algebras Open
We study (quasi-)cohomological properties through an analysis of quantum Markov semi-groups. We construct higher order Hochschild cocycles using gradient forms associated with a quantum Markov semi-group. By using Schatten-$\mathcal{S}_p$ …
View article: Tensor product decompositions and rigidity of full factors
Tensor product decompositions and rigidity of full factors Open
We obtain several rigidity results regarding tensor product decompositions of factors. First, we show that any full factor with separable predual has at most countably many tensor product decompositions up to stable unitary conjugacy. We u…
View article: Factoriality, Connes' type III invariants and fullness of amalgamated free product von Neumann algebras
Factoriality, Connes' type III invariants and fullness of amalgamated free product von Neumann algebras Open
We investigate factoriality, Connes' type ${\rm III}$ invariants and fullness of arbitrary amalgamated free product von Neumann algebras using Popa's deformation/rigidity theory. Among other things, we generalize many previous structural r…
View article: Unique prime factorization for infinite tensor product factors
Unique prime factorization for infinite tensor product factors Open
In this article, we investigate a unique prime factorization property for infinite tensor product factors. We provide several examples of type II and III factors which satisfy this property, including all free product factors with diffuse …
View article: On fundamental groups of tensor product $\rm II_1$ factors
On fundamental groups of tensor product $\rm II_1$ factors Open
Let $M$ be a $\rm II_1$ factor and let $\mathcal{F}(M)$ denote the fundamental group of $M$. In this article, we study the following property of $M$: for arbitrary $\rm II_1$ factor $B$, we have $\mathcal{F}(M \overline{\otimes} B)=\mathca…
View article: Cartan subalgebras of tensor products of free quantum group factors with arbitrary factors
Cartan subalgebras of tensor products of free quantum group factors with arbitrary factors Open
Let $\mathbb{G}$ be a free (unitary or orthogonal) quantum group. We prove that for any non-amenable subfactor $N\subset L^\infty(\mathbb{G})$, which is an image of a faithful normal conditional expectation, and for any $σ$-finite factor $…
View article: Free independence in ultraproduct von Neumann algebras and applications
Free independence in ultraproduct von Neumann algebras and applications Open
The main result of this paper is a generalization of Popa's free independence\nresult for subalgebras of ultraproduct ${\\rm II_1}$ factors [Po95] to the\nframework of ultraproduct von Neumann algebras $(M^\\omega, \\varphi^\\omega)$\nwher…
View article: Examples of factors which have no Cartan subalgebras
Examples of factors which have no Cartan subalgebras Open
We consider some conditions similar to Ozawa’s condition (AO) and prove that if a non-injective factor satisfies such a condition and has the , then it has no Cartan subalgebras. As a corollary, we prove that factors of universal orthogon…
View article: Unique prime factorization and bicentralizer problem for a class of type III factors
Unique prime factorization and bicentralizer problem for a class of type III factors Open
We show that whenever $m \geq 1$ and $M_1, \dots, M_m$ are nonamenable factors in a large class of von Neumann algebras that we call $\mathcal C_{(\text{AO})}$ and which contains all free Araki-Woods factors, the tensor product factor $M_1…